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The Poland–Scheraga model, introduced in the 1970s, is a reference model to describe the denaturation transition of DNA. More recently, it has been generalized in order to allow for asymmetry in the strands lengths and in the formation of loops: the mathematical representation is based on a bivariate renewal process, that describes the pairs of bases that bond together. Here, we consider a disordered version of the model, in which the two strands interact via a potential β V (ω ^ i , ω ¯ j) + h when the ith monomer of the first strand and the jth monomer of the second strand meet. Here, h ∈ R is a homogeneous pinning parameter, (ω i ^) i ≥ 1 and ( ω ¯ j) j ≥ 1 are two sequences of i.i.d. random variables attached to each DNA strand, V (· , ·) is an interaction function and β > 0 is the disorder intensity. In our main result, we find some condition on the underlying bivariate renewal so that, if one takes β , h ↓ 0 at some appropriate (explicit) rate as the length of the strands go to infinity, the partition function of the model admits a non-trivial, disordered, scaling limit. This is known as an intermediate disorder regime and is linked to the question of disorder relevance for the denaturation transition. Interestingly, and unlike any other model of our knowledge, the rate at which one has to take β ↓ 0 depends on the interaction function V (· , ·) and on the distribution of (ω i ^) i ≥ 1 , ( ω ¯ j) j ≥ 1 . On the other hand, the intermediate disorder limit of the partition function, when it exists, is universal: it is expressed as a chaos expansion of iterated integrals against a Gaussian process M , which arises as the scaling limit of the field (e β V (ω ^ i , ω ¯ j)) i , j ≥ 0 and exhibits correlations on lines and columns. [ABSTRACT FROM AUTHOR]

The analysis of the impact of the star polymer topology on depletion interaction potentials, depletion forces, and monomer density profiles is carried out analytically using field theory methods and techniques as well as molecular dynamic simulations. The dimensionless depletion interaction potentials and the dimensionless depletion forces for a dilute solution of ideal star polymers with three and five legs (arms) in a Θ -solvent confined in a slit between two parallel walls with repulsive surfaces and for the case where one of the surfaces is repulsive and the other inert are obtained. Furthermore, the dimensionless layer monomer density profiles for ideal star polymers with an odd number ( f ˜ = 3, 5) of arms immersed in a dilute solution of big colloidal particles with different adsorbing or repelling properties in respect of polymers are calculated, bearing in mind the Derjaguin approximation. Molecular dynamic simulations of a dilute solution of star-shaped polymers in a good solvent with N = 901 (3 × 300 + 1 -star polymer with three arms) and 1501 (5 × 300 + 1 -star polymer with five arms) beads accordingly confined in a slit with different boundary conditions are performed, and the results of the monomer density profiles for the above-mentioned cases are obtained. The numerical calculation of the radius of gyration for star polymers with f ˜ = 3, 5 arms and the ratio of the perpendicular to parallel components of the radius of gyration with respect to the wall orientation for the above-mentioned cases is performed. The obtained analytical and numerical results for star polymers with an odd number ( f ˜ = 3, 5) of arms are compared with our previous results for linear polymers in confined geometries. The acquired results show that a dilute solution of star polymer chains can be applied in the production of new functional materials, because the behavior of these solutions is strictly correlated with the topology of polymers and also with the nature and geometry of confined surfaces. The above-mentioned properties can find extensive practical application in materials engineering, as well as in biotechnology and medicine for drug and gene transmission. [ABSTRACT FROM AUTHOR]

Motivated by the experimental findings and the available recent theoretical works of two-dimensional van der Waals ferromagnets, we calculated the critical coupling strength of VI 3 and CrI 3 monolayers. We expressed the monolayer Hamiltonian as pairwise interactions with the Ising model and analyzed the problem with the renormalization group theory. We used the decimation transformation method while applying the renormalization group theory. Using the methods we developed earlier, we overcame the problem of the decimated lattice not being self-dual. Since the CrI 3 and VI 3 lattice structures are the same, the coupling constants K m , c corresponding to these monolayers were calculated as 0.383; here index m denotes either CrI 3 or VI 3 . Since the experimentally determined critical temperatures of these monolayers are also very close to each other, the exchange coupling energy J m , c corresponding to these monolayers was determined approximately as 3.2 × 10 - 22 Joule. [ABSTRACT FROM AUTHOR]

This study focuses on precisely calculating analytical critical points for rotating regular Anti-de Sitter (AdS) black holes, examining scenarios with and without external dark field contributions. Importantly, it represents the first attempt to compute critical points for this specific class of rotating black holes. Our primary focus is on investigating the impact resulting from variations in the charge of nonlinear electrodynamics on the critical phenomena of rotating regular AdS black holes, while also incorporating the influence of quintessence field contributions. The analytical investigation is concentrated on the horizon radius, employing two distinct approaches to simplify the complexity and length of the calculations. Furthermore, our examination extends to deciphering the intricate relationship between dark energy and critical phenomena. This involves visually portraying a range of critical behaviors and detailing a recent discovery regarding how the intensity of quintessence affects phase transitions. The shift in these transitions conforms to either a concave or convex function, a characteristic dependent on the sign of quintessence intensity. [ABSTRACT FROM AUTHOR]

We consider a class of nonequilibrium systems of interacting agents with pairwise interactions and quenched disorder in the dynamics featuring, in the thermodynamic limit, phase transitions. We identify mathematical conditions on the microscopic interaction structure, namely the separability of the interaction kernel, that lead to a dimension reduction of the system in terms of a finite number of reaction coordinates (RCs). Such RCs prove to be proper nonequilibrium thermodynamic variables as they carry information on correlation, memory and resilience properties of the system. Phase transitions can be identified and quantitatively characterised as singularities of the complex valued susceptibility functions associated to the RCs. We provide analytical and numerical evidence of how the singularities affect the physical properties of finite size systems. [ABSTRACT FROM AUTHOR]

We apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First, we recover the known properties of the traditional model with two-spin interactions by applying the renormalization approach for the arbitrary size of the block. For the model with three-spin couplings, we calculate the critical point and demonstrate that the phase transition is controlled by an infinite disorder fixed point. We have determined the typical correlation-length critical exponent, which seems to be different from that of the random transverse Ising chain with nearest-neighbor couplings. Thus, this model represents a new infinite disorder universality class. [ABSTRACT FROM AUTHOR]

The dynamic heterogeneities occurring just before the transition to the glassy phase have been named as the cause of amorphization in supercooled systems. Numerous studies conducted so far have confirmed this hypothesis, and based on it, a widely accepted solution to the puzzle of glass transition has been developed. This report focuses on verifying the existence of a strong pretransitional anomaly near the glass transition T g . For this purpose, supercooled liquid-crystalline systems with a strong rod-like structure were selected. Based on the obtained experimental data, we demonstrate in this article that the previously postulated dynamic heterogeneities exhibit a critical characteristic, meaning a strong pretransitional anomaly can be observed with the described critical exponent α = 0.5 . Due to this property, it can be concluded that these heterogeneities are critical fluctuations, and consequently, the transition to the glassy state can be described based on the theory of critical phenomena. To measure the pretransitional anomaly near T g in supercooled liquid-crystalline systems, broadband dielectric spectroscopy (BDS) and nonlinear dielectric effect (NDE) methods were applied. The exponent α provides insight into the nature and intensity of critical fluctuations in the system. A value of α = 0.5 suggests that the fluctuations become increasingly intense as the system approaches the critical point, contributing to the divergence in specific heat. Understanding the role of critical fluctuations in the glass transition is crucial for innovating and improving a wide range of materials for energy storage, materials design, biomedical applications, food preservation, and environmental sustainability. These advancements can lead to materials with superior properties, optimized manufacturing processes, and applications that meet the demands of modern technology and sustainability challenges. [ABSTRACT FROM AUTHOR]

We present a new wide-range correlation for the viscosity of ethene based on critically evaluated experimental data. The viscosity correlation is valid from the triple point to 450 K and up to 195 MPa. The average absolute percentage deviation of the fit for the primary data (including the critical region) is 1%, with a bias of 0.2%, The estimated uncertainty of the correlation in the gas and supercritical phases at pressures up to 195 MPa is 2.5% (at the 95% confidence level). For the dilute gas (pressures up to 0.1 MPa) in the temperature range 296 K to 450 K, the uncertainty is 0.5%. For the liquid phase at pressures up to 5.5 MPa the estimated uncertainty is 5.3%. The correlation includes a term for the critical enhancement that is significant only in a very narrow region very close to the critical point. It is less than 1% outside of the region around the critical point from 279.80 K ≤ T ≤ 290.27 K to 140.79 kg⋅m−3 ≤ ρ ≤ 293.08 kg⋅m−3. [ABSTRACT FROM AUTHOR]

Fluctuations are omnipresent; they exist in any matter, due either to its quantum nature or to its nonzero temperature. In the current review, we briefly cover the quantum electrodynamic Casimir (QED) force as well as the critical Casimir (CC) and Helmholtz (HF) forces. In the QED case, the medium is usually a vacuum and the massless excitations are photons, while in the CC and HF cases the medium is usually a critical or correlated fluid and the fluctuations of the order parameter are the cause of the force between the macroscopic or mesoscopic bodies immersed in it. We discuss the importance of the presented results for nanotechnology, especially for devising and assembling micro- or nano-scale systems. Several important problems for nanotechnology following from the currently available experimental findings are spelled out, and possible strategies for overcoming them are sketched. Regarding the example of HF, we explicitly demonstrate that when a given integral quantity characterizing the fluid is conserved, it has an essential influence on the behavior of the corresponding fluctuation-induced force. [ABSTRACT FROM AUTHOR]

Trapped bosonic atoms can be cooled down to temperatures where the atomic cloud experiences Bose–Einstein condensation. Almost all atoms in a dilute gaseous system can be Bose-condensed, which implies that this system is in a coherent state. The coherent atomic system enjoys many properties typical of coherent optical systems. It is possible to generate different condensate coherent modes similarly to the generation of optical modes. Several effects can be observed, such as interference patterns, interference current, Rabi oscillations, harmonic generation, parametric conversion, Ramsey fringes, mode locking, dynamic transition between Rabi and Josephson regimes, and atomic squeezing. [ABSTRACT FROM AUTHOR]

We study the critical behaviors of systems undergoing fractal time processes above the upper critical dimension. We derive a set of novel critical exponents, irrespective of the order of the fractional time derivative or the particular form of interaction in the Hamiltonian. For fractal time processes, we not only discover new universality classes with a dimensional constant but also decompose the dangerous irrelevant variables to obtain corrections for critical dynamic behavior and static critical properties. This contrasts with the traditional theory of critical phenomena, which posits that static critical exponents are unrelated to the dynamical processes. Simulations of the Landau–Ginzburg model for fractal time processes and the Ising model with temporal long-range interactions both show good agreement with our set of critical exponents, verifying its universality. The discovery of this new universality class provides a method for examining whether a system is undergoing a fractal time process near the critical point. [ABSTRACT FROM AUTHOR]

Can liquid-like and gas-like states be distinguished beyond the critical point, where the liquid--gas phase transition no longer exists and conventionally only a single supercritical fluid phase is defined? Recent experiments and simulations report strong evidence of dynamical crossovers above the critical temperature and pressure. Despite using different criteria, many existing theoretical explanations consider a single crossover line separating liquid-like and gas-like states in the supercritical fluid phase. We argue that such a single-line scenario is inconsistent with the supercritical behavior of the Ising model, which has two crossover lines due to its symmetry, violating the universality principle of critical phenomena. To reconcile the inconsistency, we define two thermodynamic crossover lines in supercritical fluids as boundaries of liquid-like, indistinguishable, and gas-like states. Near the critical point, the two crossover lines follow critical scalings with exponents of the Ising universality class, supported by calculations of theoretical models and analyses of experimental data from the standard database. The upper line agrees with crossovers independently estimated from the inelastic X-ray scattering data of supercritical argon, and from the small-angle neutron scattering data of supercritical carbon dioxide. The lower line is verified by the equation of states for the compressibility factor. This work provides a fundamental framework for understanding supercritical physics in general phase transitions. [ABSTRACT FROM AUTHOR]

The report presents static, low-frequency, and dynamic dielectric properties in the isotropic liquid, nematic, and solid phases of MBBA and related nanocolloids with paraelectric BaTiO3 nanoparticles (spherical, d = 50 nm). MBBA (4-methoxybenzylidene-4′–butylaniline) is a liquid crystalline compound with a permanent dipole moment transverse to the long molecular axis. The distortions-sensitive analysis of the dielectric constant revealed its hidden pretransitional anomaly, strongly influenced by the addition of nanoparticles. The evolution of the dielectric constant in the nematic phase shows the split into two regions, with the crossover coinciding with the standard melting temperature. The 'universal' exponential-type behavior of the low-frequency contribution to the real part of the dielectric permittivity is found. The critical-like pretransitional behavior in the solid phase is also evidenced. This is explained by linking the Lipovsky model to the Mossotti catastrophe concept under quasi-negative pressure conditions. The explicit preference for the 'critical-like' evolution of the apparent activation enthalpy is worth stressing for dynamics. Finally, the long-range, 'critical-like' behavior of the dissipation factor (D = tgδ), covering the isotropic liquid and nematic phases, is shown. [ABSTRACT FROM AUTHOR]

We pursue the analysis of nesting statistics in the O.n/loop model on random maps, initiated for maps with the topology of disks and cylinders by Borot, Bouttier and Duplantier (2016), here for arbitrary topologies. For this purpose, we rely on the topological recursion results by Borot, Eynard and Orantin (2011, 2015) for the enumeration of maps in the O.n/model. We characterize the generating series of maps of genus g with k boundaries and k0 marked points which realize a fixed nesting graph. These generating series are amenable to explicit computations in the loop model with bending energy on triangulations, and we characterize their behavior at criticality in the dense and in the dilute phase. [ABSTRACT FROM AUTHOR]

The long-range supercritical changes of dielectric constant, resembling ones observed in the isotropic liquid phase of liquid crystalline compounds, are evidenced for linseed oil—although in the given case, the phenomenon is associated with the liquid–solid melting/freezing discontinuous phase transitions. This 'supercriticality' can be an additional factor supporting the unique pro-health properties of linseed oil. Broadband dielectric spectroscopy studies also revealed the 'glassy' changes of relaxation times, well portrayed by the 'activated and critical' equation recently introduced. In the solid phase, the premelting effect characteristic for the canonic melting/freezing discontinuous transition, i.e., without any pretransitional effect in the liquid phase, has been detected. It is interpreted within the grain model, and its parameterization is possible using the Lipovsky model and the 'reversed' Mossotti catastrophe concept. For the premelting effect in the solid state, the singular 'critical' temperature correlates with the bulk discontinuous melting and freezing temperatures. Consequently, the report shows that linseed oil, despite its 'natural and complex' origins, can be considered a unique model system for two fundamental problems: (i) pretransitional (supercritical) effects in the liquid state associated with a weakly discontinuous phase transition, and (ii) the premelting behavior in the solid side of the discontinuous melting/freezing discontinuous transition. [ABSTRACT FROM AUTHOR]

A spread-out lattice animal is a finite connected set of edges in $\{\{x,y\}\subset \mathbb{Z}^d\;:\;0\lt \|x-y\|\le L\}$. A lattice tree is a lattice animal with no loops. The best estimate on the critical point $p_{\textrm{c}}$ so far was achieved by Penrose (J. Stat. Phys. 77, 3–15, 1994) : $p_{\textrm{c}}=1/e+O(L^{-2d/7}\log L)$ for both models for all $d\ge 1$. In this paper, we show that $p_{\textrm{c}}=1/e+CL^{-d}+O(L^{-d-1})$ for all $d\gt 8$ , where the model-dependent constant $C$ has the random-walk representation \begin{align*} C_{\textrm{LT}}=\sum _{n=2}^\infty \frac{n+1}{2e}U^{*n}(o),&& C_{\textrm{LA}}=C_{\textrm{LT}}-\frac 1{2e^2}\sum _{n=3}^\infty U^{*n}(o), \end{align*} where $U^{*n}$ is the $n$ -fold convolution of the uniform distribution on the $d$ -dimensional ball $\{x\in{\mathbb R}^d\;: \|x\|\le 1\}$. The proof is based on a novel use of the lace expansion for the 2-point function and detailed analysis of the 1-point function at a certain value of $p$ that is designed to make the analysis extremely simple. [ABSTRACT FROM AUTHOR]

The long-range supercritical changes of dielectric constant, resembling ones observed in the isotropic liquid phase of liquid crystalline compounds, are evidenced for linseed oil—although in the given case, the phenomenon is associated with the liquid–solid melting/freezing discontinuous phase transitions. This ‘supercriticality’ can be an additional factor supporting the unique pro-health properties of linseed oil. Broadband dielectric spectroscopy studies also revealed the ‘glassy’ changes of relaxation times, well portrayed by the ‘activated and critical’ equation recently introduced. In the solid phase, the premelting effect characteristic for the canonic melting/freezing discontinuous transition, i.e., without any pretransitional effect in the liquid phase, has been detected. It is interpreted within the grain model, and its parameterization is possible using the Lipovsky model and the ‘reversed’ Mossotti catastrophe concept. For the premelting effect in the solid state, the singular ‘critical’ temperature correlates with the bulk discontinuous melting and freezing temperatures. Consequently, the report shows that linseed oil, despite its ‘natural and complex’ origins, can be considered a unique model system for two fundamental problems: (i) pretransitional (supercritical) effects in the liquid state associated with a weakly discontinuous phase transition, and (ii) the premelting behavior in the solid side of the discontinuous melting/freezing discontinuous transition.

The analysis of the impact of the star polymer topology on depletion interaction potentials, depletion forces, and monomer density profiles is carried out analytically using field theory methods and techniques as well as molecular dynamic simulations. The dimensionless depletion interaction potentials and the dimensionless depletion forces for a dilute solution of ideal star polymers with three and five legs (arms) in a Θ-solvent confined in a slit between two parallel walls with repulsive surfaces and for the case where one of the surfaces is repulsive and the other inert are obtained. Furthermore, the dimensionless layer monomer density profiles for ideal star polymers with an odd number (f˜ = 3, 5) of arms immersed in a dilute solution of big colloidal particles with different adsorbing or repelling properties in respect of polymers are calculated, bearing in mind the Derjaguin approximation. Molecular dynamic simulations of a dilute solution of star-shaped polymers in a good solvent with N = 901 (3 × 300 + 1 -star polymer with three arms) and 1501 (5 × 300 + 1 -star polymer with five arms) beads accordingly confined in a slit with different boundary conditions are performed, and the results of the monomer density profiles for the above-mentioned cases are obtained. The numerical calculation of the radius of gyration for star polymers with f˜ = 3, 5 arms and the ratio of the perpendicular to parallel components of the radius of gyration with respect to the wall orientation for the above-mentioned cases is performed. The obtained analytical and numerical results for star polymers with an odd number (f˜ = 3, 5) of arms are compared with our previous results for linear polymers in confined geometries. The acquired results show that a dilute solution of star polymer chains can be applied in the production of new functional materials, because the behavior of these solutions is strictly correlated with the topology of polymers and also with the nature and geometry of confined surfaces. The above-mentioned properties can find extensive practical application in materials engineering, as well as in biotechnology and medicine for drug and gene transmission.

During cell division, precise and regulated distribution of cellular material between daughter cells is a critical step and is governed by complex biochemical and biophysical mechanisms. To achieve this, membraneless organelles and condensates often require complete disassembly during mitosis. The biophysical principles governing the disassembly of condensates remain poorly understood. Here, we used a physical biology approach to study how physical and material properties of the nucleolus, a prominent nuclear membraneless organelle in eukaryotic cells, change during mitosis and across different scales. We found that nucleolus disassembly proceeds continuously through two distinct phases with a slow and reversible preparatory phase followed by a rapid irreversible phase that was concurrent with the nuclear envelope breakdown. We measured microscopic properties of nucleolar material including effective diffusion rates and binding affinities as well as key macroscopic properties of surface tension and bending rigidity. By incorporating these measurements into the framework of critical phenomena, we found evidence that near mitosis surface tension displays a power-law behavior as a function of biochemically modulated interaction strength. This two-step disassembly mechanism maintains structural and functional stability of nucleolus while enabling its rapid and efficient disassembly in response to cell cycle cues. [ABSTRACT FROM AUTHOR]

Selma Lagerlöf said that culture is what remains when one has forgotten everything we had learned. Without any warranty, through ongoing research tasks, that I will ever attain this high level of wisdom, I simply share here reminiscences that have played, during my life, an important role in my incursions in science, mainly in theoretical physics. I end by presenting some perspectives for future developments. [ABSTRACT FROM AUTHOR]

Large, open‐gate transistors made from metal nanoparticle arrays offer possibilities to build new electronic devices, such as sensors. A nanoparticle necklace network (N3) of Au particles from 300 K to cryogenic temperatures exhibit a nonohmic I–Vd behavior, I ≈ (Vd–VT)ζ, where VT is a conduction gap and ζ is a constant critical exponent. The conduction gap in N3, made from disordered networks of 1D chains of 10 nm diameter Au particles exhibits room temperature (RT) gating. Although the I–Vd behavior at RT is identical to Coulomb blockade, the conduction is modulated by field‐assisted tunneling exhibiting classical critical behavior. In this study, based on three results, invariance of VT on gating, invariance of VT on temperature, and zero–bias conductance, a sharp transition temperature at ≈140 K is discovered where the conduction mechanism switches from Coulomb blockade to classical critical percolation behavior. The N3 architecture allows the reconciliation of the Coulomb blockade versus activation process as a sharp thermal transition to serve as a model system to study the exotic behavior in nanogranular‐metallic materials. The novel global critical behavior to local Coulomb blockade governed transition in these N3 architectures may potentially lead to novel sensors and biosensors. [ABSTRACT FROM AUTHOR]

This model discussion focuses on links between the unique properties of relaxor ceramics and the basics of Critical Phenomena Physics and Glass Transition Physics. It indicates the significance of uniaxiality for the appearance of mean-field type features near the paraelectric-to-ferroelectric phase transition. Pretransitional fluctuations, that are increasing up to the size of a grain and leading to inter-grain, random, local electric fields are responsible for relaxor ceramics characteristics. Their impact yields the pseudospinodal behavior associated with "weakly discontinuous" local phase transitions. The emerging model redefines the meaning of the Burns temperature and polar nanoregions (PNRs). It offers a coherent explanation of "dielectric constant" changes with the "diffused maximum" near the paraelectric-to-ferroelectric transition, the sensitivity to moderate electric fields (tunability), and the "glassy" dynamics. These considerations are challenged by the experimental results of complex dielectric permittivity studies in a Ba0.65Sr0.35TiO3 relaxor ceramic, covering ca. 250 K, from the paraelectric to the "deep" ferroelectric phase. The distortion-sensitive and derivative-based analysis in the paraelectric phase and the surrounding paraelectric-to-ferroelectric transition reveal a preference for the exponential scaling pattern for ε(T) changes. This may suggest that Griffith-phase behavior is associated with mean-field criticality disturbed by random local impacts. The preference for the universalistic "critical & activated" evolution of the primary relaxation time is shown for dynamics. The discussion is supplemented by a coupled energy loss analysis. The electric field-related tunability studies lead to scaling relationships describing their temperature changes. [ABSTRACT FROM AUTHOR]

The commonly quoted bistable Higgs potential is not a proper description of the Higgs field because, among other technical reasons, one of its stable states acquires a negative expectation value in vacuum. We rely on formal catastrophe theory to derive the form of the Higgs potential that admits only one positive mean value in vacuum. No symmetry is broken during the ensuing phase transition that assigns mass to the Higgs field; only gauge redundancy is "broken" by the appearance of phase in the massive state, but this redundancy is not a true symmetry of the massless field. Furthermore, a secondary, certainly amusing conclusion, is that, in its high-energy state, the field oscillates about its potential minimum between positive and negative masses, but it is doubtful that such evanescent states can survive below the critical temperature of 159.5 GeV, where the known particles were actually created. [ABSTRACT FROM AUTHOR]

To understand how the temporal non-locality («memory») properties of a process affect its critical regimes, the power-law compound and time-fractional Poisson process is presented as a universal hereditary model of criticality. Seismicity is considered as an application of the theory of criticality. On the basis of the proposed hereditarian criticality model, the critical regimes of seismicity are investigated. It is shown that the seismic process has the property of «memory» (non-locality over time) and statistical time-dependence of events. With a decrease in the fractional exponent of the Poisson process, the relaxation slows down, which can be associated with the hardening of the medium and the accumulation of elastic energy. Delayed relaxation is accompanied by an abnormal increase in fluctuations, which is caused by the non-local correlations of random events over time. According to the found criticality indices, the seismic process is in subcritical regimes for the zero and first moments and in supercritical regimes for the second statistical moment of events' reoccurrence frequencies distribution. The supercritical regimes indicate the instability of the deformation changes that can go into a non-stationary regime of a seismic process. [ABSTRACT FROM AUTHOR]

We apply a real-space block renormalization group approach to study the critical properties of the random transverse-field Ising spin chain with multispin interactions. First, we recover the known properties of the traditional model with two-spin interactions by applying the renormalization approach for the arbitrary size of the block. For the model with three-spin couplings, we calculate the critical point and demonstrate that the phase transition is controlled by an infinite disorder fixed point. We have determined the typical correlation-length critical exponent, which seems to be different from that of the random transverse Ising chain with nearest-neighbor couplings. Thus, this model represents a new infinite disorder universality class.

The dynamic heterogeneities occurring just before the transition to the glassy phase have been named as the cause of amorphization in supercooled systems. Numerous studies conducted so far have confirmed this hypothesis, and based on it, a widely accepted solution to the puzzle of glass transition has been developed. This report focuses on verifying the existence of a strong pretransitional anomaly near the glass transition Tg. For this purpose, supercooled liquid-crystalline systems with a strong rod-like structure were selected. Based on the obtained experimental data, we demonstrate in this article that the previously postulated dynamic heterogeneities exhibit a critical characteristic, meaning a strong pretransitional anomaly can be observed with the described critical exponent α=0.5. Due to this property, it can be concluded that these heterogeneities are critical fluctuations, and consequently, the transition to the glassy state can be described based on the theory of critical phenomena. To measure the pretransitional anomaly near Tg in supercooled liquid-crystalline systems, broadband dielectric spectroscopy (BDS) and nonlinear dielectric effect (NDE) methods were applied. The exponent α provides insight into the nature and intensity of critical fluctuations in the system. A value of α=0.5 suggests that the fluctuations become increasingly intense as the system approaches the critical point, contributing to the divergence in specific heat. Understanding the role of critical fluctuations in the glass transition is crucial for innovating and improving a wide range of materials for energy storage, materials design, biomedical applications, food preservation, and environmental sustainability. These advancements can lead to materials with superior properties, optimized manufacturing processes, and applications that meet the demands of modern technology and sustainability challenges.

Fluctuations are omnipresent; they exist in any matter, due either to its quantum nature or to its nonzero temperature. In the current review, we briefly cover the quantum electrodynamic Casimir (QED) force as well as the critical Casimir (CC) and Helmholtz (HF) forces. In the QED case, the medium is usually a vacuum and the massless excitations are photons, while in the CC and HF cases the medium is usually a critical or correlated fluid and the fluctuations of the order parameter are the cause of the force between the macroscopic or mesoscopic bodies immersed in it. We discuss the importance of the presented results for nanotechnology, especially for devising and assembling micro- or nano-scale systems. Several important problems for nanotechnology following from the currently available experimental findings are spelled out, and possible strategies for overcoming them are sketched. Regarding the example of HF, we explicitly demonstrate that when a given integral quantity characterizing the fluid is conserved, it has an essential influence on the behavior of the corresponding fluctuation-induced force.

Abstract Large, open‐gate transistors made from metal nanoparticle arrays offer possibilities to build new electronic devices, such as sensors. A nanoparticle necklace network (N3) of Au particles from 300 K to cryogenic temperatures exhibit a nonohmic I–Vd behavior, I ≈ (Vd–VT)ζ, where VT is a conduction gap and ζ is a constant critical exponent. The conduction gap in N3, made from disordered networks of 1D chains of 10 nm diameter Au particles exhibits room temperature (RT) gating. Although the I–Vd behavior at RT is identical to Coulomb blockade, the conduction is modulated by field‐assisted tunneling exhibiting classical critical behavior. In this study, based on three results, invariance of VT on gating, invariance of VT on temperature, and zero–bias conductance, a sharp transition temperature at ≈140 K is discovered where the conduction mechanism switches from Coulomb blockade to classical critical percolation behavior. The N3 architecture allows the reconciliation of the Coulomb blockade versus activation process as a sharp thermal transition to serve as a model system to study the exotic behavior in nanogranular‐metallic materials. The novel global critical behavior to local Coulomb blockade governed transition in these N3 architectures may potentially lead to novel sensors and biosensors.

Quantum networks have experienced rapid advancements in both theoretical and experimental domains over the last decade, making it increasingly important to understand their large-scale features from the viewpoint of statistical physics. This review paper discusses a fundamental question: how can entanglement be effectively and indirectly (e.g., through intermediate nodes) distributed between distant nodes in an imperfect quantum network, where the connections are only partially entangled and subject to quantum noise? We survey recent studies addressing this issue by drawing exact or approximate mappings to percolation theory, a branch of statistical physics centered on network connectivity. Notably, we show that the classical percolation frameworks do not uniquely define the network's indirect connectivity. This realization leads to the emergence of an alternative theory called "concurrence percolation", which uncovers a previously unrecognized quantum advantage that emerges at large scales, suggesting that quantum networks are more resilient than initially assumed within classical percolation contexts, offering refreshing insights into future quantum network design. [ABSTRACT FROM AUTHOR]

We study the critical behaviors of systems undergoing fractal time processes above the upper critical dimension. We derive a set of novel critical exponents, irrespective of the order of the fractional time derivative or the particular form of interaction in the Hamiltonian. For fractal time processes, we not only discover new universality classes with a dimensional constant but also decompose the dangerous irrelevant variables to obtain corrections for critical dynamic behavior and static critical properties. This contrasts with the traditional theory of critical phenomena, which posits that static critical exponents are unrelated to the dynamical processes. Simulations of the Landau–Ginzburg model for fractal time processes and the Ising model with temporal long-range interactions both show good agreement with our set of critical exponents, verifying its universality. The discovery of this new universality class provides a method for examining whether a system is undergoing a fractal time process near the critical point.

The report presents static, low-frequency, and dynamic dielectric properties in the isotropic liquid, nematic, and solid phases of MBBA and related nanocolloids with paraelectric BaTiO3 nanoparticles (spherical, d = 50 nm). MBBA (4-methoxybenzylidene-4′–butylaniline) is a liquid crystalline compound with a permanent dipole moment transverse to the long molecular axis. The distortions-sensitive analysis of the dielectric constant revealed its hidden pretransitional anomaly, strongly influenced by the addition of nanoparticles. The evolution of the dielectric constant in the nematic phase shows the split into two regions, with the crossover coinciding with the standard melting temperature. The ‘universal’ exponential-type behavior of the low-frequency contribution to the real part of the dielectric permittivity is found. The critical-like pretransitional behavior in the solid phase is also evidenced. This is explained by linking the Lipovsky model to the Mossotti catastrophe concept under quasi-negative pressure conditions. The explicit preference for the ‘critical-like’ evolution of the apparent activation enthalpy is worth stressing for dynamics. Finally, the long-range, ‘critical-like’ behavior of the dissipation factor (D = tgδ), covering the isotropic liquid and nematic phases, is shown.

This work explores the spectral behavior of interacting many-body systems — gravitating dust solutions (galaxy formations and black hole clusters) and Brownian fluids. The eigenvalue dynamics of these systems are then represented by the two-dimensional Yang–Mills field (i.e. spectral projection). The interacting particles in the many-body systems are associated with random matrices of dimensions, N. The Painlevé II dynamical system is shown to surface at large N (N → ∞); when the mentioned Yang–Mills field is configured in a specific way. Critical phenomena (Douglas–Kazakov phase transition) of the interacting many-body systems at large N were attained via the spectral projection of the mentioned physical systems. In addition, the existence of instantons (spectral Dirac monopoles) in the strong coupling phase was shown during phase transition. [ABSTRACT FROM AUTHOR]

The finite-size scaling (FSS) theory is a relatively new and important attempt to study critical phenomena; this paper aims to contribute to clarifying the philosophical significance of this theory. We maintain that, contrary to initial appearances and to some recent claims in the literature, the FSS theory cannot arbitrate the debate between the reductionists and anti-reductionists about phase transitions. Although the theory allows scientists to provide predictions for finite systems, the analysis we carry on here shows that it involves the intertwinement of both finite and infinite systems. But, we argue, the FSS theory has another virtue, as it provides quantitative predictions and explanations for finite systems close to the critical point; it thus complements in a distinctive manner the standard Renormalization Group qualitative approach relying on infinite systems. [ABSTRACT FROM AUTHOR]

The chiral Potts model is studied by means of the real space renormalization group. We use the renormalization group scheme proposed by Niemeyer and Van Leeuwen with an approximation that retains only the first term in the cumulant expansion. The recurrence relations are obtained for any number of states, renormalization factor and lattice dimension. By using a renormalization factor b = 4 , the phase diagram for the three-state model on a square lattice is obtained in terms of the chiral field and temperature. It shows two regions: a disordered one, which corresponds to the paramagnetic phase, and a modulated one, consisting of structures described by rational wave numbers. [ABSTRACT FROM AUTHOR]

Equilibrium molecular dynamics (EMD) simulations are used to model density ρL, dynamic viscosity ηL, and self-diffusivity Dself of liquid ethane at pressures close to saturation conditions and temperatures T between (184–298) K, close to the critical temperature Tc. To correct for a T-dependent drift of the simulated results from experimental data, a T-dependent force field modification from our previous studies is extended to a wider T-range. The modification is validated within this work by comparing predicted ρL, ηL, and Dself to experimental reference data. With the modification applied, EMD simulations are able to predict ρL, ηL, and Dself of liquid ethane at T = 298 K with relative deviations of 6.3%, 13%, and 28% from literature references, respectively. Simulations of binary mixtures of liquid ethane with different dissolved gases were performed to predict the Fick diffusivity D11. At a mole fraction of dissolved nitrogen xN2 = 0.03, a deviation of more than a factor of three is found between simulation results and experimental results determined using the dynamic light scattering method. This shows that EMD simulations are not able to predict the critical slowing down of D11 approaching Tc, despite excellent agreement between simulations and reference data for neat ethane. [ABSTRACT FROM AUTHOR]

This paper presents new wide-ranging correlations for the viscosity and thermal conductivity of 1-hexene based on critically evaluated experimental data. The viscosity correlation is valid from the triple point to 580 K and up to 245 MPa pressure, while the thermal conductivity is valid from the triple point to 620 K and 200 MPa pressure. Both correlations are designed to be used with a recently published equation of state that extends from the triple point to 535 K, at pressures up to 245 MPa. The estimated uncertainty (at a 95 % confidence level) for the viscosity is 2 % for the low-density gas (pressures below 0.5 MPa), and 4.8 % over the rest of the range of application. For thermal conductivity, the expanded uncertainty is estimated to be 3 % for the low-density gas and 4 % over the rest of the range. [ABSTRACT FROM AUTHOR]

It has recently become appreciated that cells self-organize their interiors through the formation of biomolecular condensates. These condensates, typically formed through liquid-liquid phase separation of proteins, nucleic acids, and other biopolymers, exhibit reversible assembly/disassembly in response to changing conditions. Condensates play many functional roles, aiding in biochemical reactions, signal transduction, and sequestration of certain components. Ultimately, these functions depend on the physical properties of condensates, which are encoded in the microscopic features of the constituent biomolecules. In general, the mapping from microscopic features to macroscopic properties is complex, but it is known that near a critical point, macroscopic properties follow power laws with only a small number of parameters, making it easier to identify underlying principles. How far does this critical region extend for biomolecular condensates and what principles govern condensate properties in the critical regime? Using coarse-grained molecular-dynamics simulations of a representative class of biomolecular condensates, we found that the critical regime can be wide enough to cover the full physiological range of temperatures. Within this critical regime, we identified that polymer sequence influences surface tension predominately via shifting the critical temperature. Finally, we show that condensate surface tension over a wide range of temperatures can be calculated from the critical temperature and a single measurement of the interface width. [ABSTRACT FROM AUTHOR]

We explore the critical and scaling behavior of delayed bifurcations in systems with dynamic disorder well-known in kinetics when the control parameter in the rate is made to sweep stochastically across the critical point. The analysis is based on an extended Hamiltonian system that includes noise as an additional degree of freedom conjugate to the relevant dynamical variable. Appropriate quantifiers for measuring the time delay in reaching the bifurcation point have been introduced. We show that the time delay (i.e., the time difference between the static and dynamic bifurcation times) exhibits a power law decay with the deviation of the control parameter from its critical value, the decay constant being close to unity and is independent of the nature of bifurcations. The characteristic time to reach the zero solution state decreases algebraically with the deviation of the dynamical variable from its critical value and the decay exponent scales as the highest power of nonlinearity characterizing the nature of bifurcations. Bifurcations are essential features of various chemical kinetics; biological and ecological evolution. Critical and scaling behavior of delayed bifurcations in such systems with dynamic disorder has been explored when the control parameter in the rate is varied stochastically across the critical point. [ABSTRACT FROM AUTHOR]

Numerical calculations of two component cellular convection with a lighter component diffusing down from the top are a simple model of the convection of rocky planets with a crust. The crust either is mixed down, floats along the top as blobs (continents separated by ocean basins), or forms layers. The calculations are for very viscous fluid with density variations from temperature and the lighter component representing the crust. If variations are approximately the same size, the lighter component collects along the top into H‐shaped blobs/clusters that have a flat midsection with two lobes on each end. Elevations are calculated for a free upper surface and the shape resembles continent and ocean floor topography with level interiors and thickening (mountains) at the edges produced by sinking at the margins. Between each pair of clusters, thermal and concentration boundary layers resemble ocean basins with spreading centers. Convection is unsteady but introducing internal decay of the lighter concentration produces steady flow. Internal heating produces similar results along with periodic drifting and merging of blobs like some geological cycles. The fact that these features arise without phase changes or viscosity variation implies that blobs of continent‐like crust might be widely found on rocky planets. Plain Language Summary: A simple numerical model of fluid flow has circulation cells driven by buoyancy. The cells are propelled by convection cells like mantle convection. Along the top, a model of a crust with lower density accumulates into a row of shapes. These resemble continents separated by ocean basins. Each accumulation is shaped like a wide capital letter H with a middle plateau and thickening (like mountains) at both ends. Cold, dense surface fluid plunges down next to each end like ocean trenches and subduction zones. These accumulations extend above the fluid surface because of their low density. Midway between each pair of these accumulations, hot fluid rises from the bottom and spreads out. The surface is depressed like ocean basins although the center is slightly elevated like mid‐ocean ridges. Forming these features from flow of a single constant viscosity fluid has not been previously done so the dynamics are discussed. Key Points: Convection cells with lighter fluid diffusing down from the top produce shapes like continents and ocean basins for certain parametersAdding internal heating produces cycles of splitting, drifting, and merging like the Wilson cycleThe calculations are simple and include two diffusivities for temperature and composition. A MATLAB code is included [ABSTRACT FROM AUTHOR]

In any medium there are fluctuations due to temperature or due to the quantum nature of its constituents. If a material body is immersed into such a medium, its shape and the properties of its constituents modify the properties of the surrounding medium and its fluctuations. If in the same medium there is a second body then — in addition to all direct interactions between them — the modifications due to the first body influence the modifications due to the second body. This mutual influence results in a force between these bodies. If the excitations of the medium, which mediate the effective interaction between the bodies, are massless, this force is long-ranged and nowadays known as a Casimir force. If the fluctuating medium consists of the confined electromagnetic field in vacuum, one speaks of the quantum mechanical Casimir effect. In the case that the order parameter of material fields fluctuates – such as differences of number densities or concentrations – and that the corresponding fluctuations of the order parameter are long-ranged, one speaks of the critical Casimir effect. This holds, e.g., in the case of systems which undergo a second-order phase transition and which are thermodynamically located near the corresponding critical point, or for systems with a broken continuous symmetry exhibiting Goldstone mode excitations. Here we review the currently available exact results concerning the critical Casimir effect in systems encompassing the one-dimensional Ising, XY, and Heisenberg models, the two-dimensional Ising model, the Gaussian and the spherical models, as well as the mean field results for the Ising and the XY model. Special attention is paid to the influence of the boundary conditions on the behavior of the Casimir force. We present results both for the case of classical critical fluctuations if the system possesses a critical point at a non-zero temperature, as well as the case of quantum systems undergoing a continuous phase transition at zero temperature as function of certain parameters. As confinements we consider the film, the sphere–plane, and the sphere–sphere geometries. We discuss systems governed by short-ranged, by subleading long-ranged (i.e., of the van der Waals type), and by leading long-ranged interactions. In order to put the critical Casimir effect into the proper context and in order to make the review as self-contained as possible, basic facts about the theory of phase transitions, the theory of critical phenomena in classical and quantum systems, and finite-size scaling theory are recalled. Whenever possible, a discussion of the relevance of the exact results towards an understanding of available experiments is presented. The eventual applicability of the present results for certain devices is pointed out, too. [ABSTRACT FROM AUTHOR]

Selma Lagerlöf said that culture is what remains when one has forgotten everything we had learned. Without any warranty, through ongoing research tasks, that I will ever attain this high level of wisdom, I simply share here reminiscences that have played, during my life, an important role in my incursions in science, mainly in theoretical physics. I end by presenting some perspectives for future developments.

To understand how the temporal non-locality («memory») properties of a process affect its critical regimes, the power-law compound and time-fractional Poisson process is presented as a universal hereditary model of criticality. Seismicity is considered as an application of the theory of criticality. On the basis of the proposed hereditarian criticality model, the critical regimes of seismicity are investigated. It is shown that the seismic process has the property of «memory» (non-locality over time) and statistical time-dependence of events. With a decrease in the fractional exponent of the Poisson process, the relaxation slows down, which can be associated with the hardening of the medium and the accumulation of elastic energy. Delayed relaxation is accompanied by an abnormal increase in fluctuations, which is caused by the non-local correlations of random events over time. According to the found criticality indices, the seismic process is in subcritical regimes for the zero and first moments and in supercritical regimes for the second statistical moment of events’ reoccurrence frequencies distribution. The supercritical regimes indicate the instability of the deformation changes that can go into a non-stationary regime of a seismic process.

This model discussion focuses on links between the unique properties of relaxor ceramics and the basics of Critical Phenomena Physics and Glass Transition Physics. It indicates the significance of uniaxiality for the appearance of mean-field type features near the paraelectric-to-ferroelectric phase transition. Pretransitional fluctuations, that are increasing up to the size of a grain and leading to inter-grain, random, local electric fields are responsible for relaxor ceramics characteristics. Their impact yields the pseudospinodal behavior associated with “weakly discontinuous” local phase transitions. The emerging model redefines the meaning of the Burns temperature and polar nanoregions (PNRs). It offers a coherent explanation of “dielectric constant” changes with the “diffused maximum” near the paraelectric-to-ferroelectric transition, the sensitivity to moderate electric fields (tunability), and the “glassy” dynamics. These considerations are challenged by the experimental results of complex dielectric permittivity studies in a Ba0.65Sr0.35TiO3 relaxor ceramic, covering ca. 250 K, from the paraelectric to the “deep” ferroelectric phase. The distortion-sensitive and derivative-based analysis in the paraelectric phase and the surrounding paraelectric-to-ferroelectric transition reveal a preference for the exponential scaling pattern for ε(T) changes. This may suggest that Griffith-phase behavior is associated with mean-field criticality disturbed by random local impacts. The preference for the universalistic “critical & activated” evolution of the primary relaxation time is shown for dynamics. The discussion is supplemented by a coupled energy loss analysis. The electric field-related tunability studies lead to scaling relationships describing their temperature changes.

A large-scale renormalization group study of the Ising model for the square, honeycomb, triangular, simple cubic, and body-centered (BC) cubic lattices has been performed recently by us. We complement those studies with the structurally more complicated face-centered cubic lattice Ising model. The results obtained from the real space renormalization group (RSRG) treatment of the face-centered simple cubic (FCSC) Ising lattice have been presented in this work. The difficulty due to its non-self-dual decimation transformation property and high numbers of nearest neighbors in the treatment is overcome with some relevant approximations. The approximation is based on keeping only the pairwise interactions in the decimated lattice which is apparently in the form of a tetragonal structure. Within this approximation, the renormalized coupling strength is related to the coupling constant of the original lattice. The critical coupling strength for the decimated tetragonal structure is calculated as 0.0905. [ABSTRACT FROM AUTHOR]

The critical O (N) CFT in spacetime dimensions 2 < d < 4 is one of the most important examples of a conformal field theory, with the Ising CFT at N = 1 , 2 ⩽ d < 4 , as a notable special case. Apart from numerous physical applications, it serves frequently as a concrete testing ground for new approaches and techniques based on conformal symmetry. In the perturbative limits – the 4 − ɛ expansion, the large N expansion and the 2 + ϵ ̃ expansion – a lot of conformal data have been computed over the years. In this report, we give an overview of the critical O (N) CFT, including some methods to study it, and present a large collection of conformal data. The data, extracted from the literature and supplemented by many additional computations of order ɛ anomalous dimensions, are made available through an ancillary data file. [ABSTRACT FROM AUTHOR]