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Graphical abstract, While swarming behavior is regarded as a critical phenomenon in phase transition and frequently shows the properties of a critical state such as Lévy walk, a general mechanism to explain the critical property in swarming behavior has not yet been found. Here, we address this problem with a simple swarm model, the Self-Propelled Particle (SPP) model, and propose a way to explain this critical behavior by introducing agents making decisions via the data-hypothesis interaction in Bayesian inference, namely, Bayesian and inverse Bayesian inference (BIB). We compare three SPP models, namely, the simple SPP, the SPP with Bayesian-only inference (BO) and the SPP with BIB models. We show that only the BIB model entails coexisting tornado, splash and translation behaviors, and the Lévy walk pattern.

Thermodynamics is a science concerning the state of a system, whether it is stable, metastable or unstable, when interacting with the surroundings. In this overview, fundamentals of thermodynamics are briefly reviewed through the combination of first and second laws of thermodynamics for open and nonequilibrium systems to demonstrate that the reversible equilibrium and irreversible nonequilibrium thermodynamics can be integrated to enhance the power and utilities of thermodynamics. The recent progresses in computational thermodynamics, the remaining challenges, and potential impacts in broad scientific fields are discussed. It is shown that computational thermodynamics enables the modeling of thermodynamics of a state as a function of both external and internal variables and quantitative calculations of a broad range of properties of a multicomponent system in terms of first and second derivatives of energy, including not only equilibrium states when there are no driving forces for any internal processes and but also non-equilibrium states with driving forces for internal processes. Consequently, external constraints such as fixed strain and internal degree of freedoms such as ordering and defects can be described in a coherent framework and applied to materials design. Furthermore, two important but largely overlooked aspects in thermodynamics will be discussed, i.e. the rigorous application of statistical thermodynamics with the probability of configurations and their contributions to system properties, and the applications of second derivatives of energy with respect to either two extensive variables or two potentials or a mixture of them in terms of understanding and predicting emergent behaviors, critical phenomena, kinetic coefficients, and mechanical properties.

The isobaric heat capacity and the coefficient of thermal expansion of a binary liquid mixture with a critical point of solution diverge as functions of temperature in the critical region. When the same liquids are used as solvents for chemical reactions, the van’t Hoff plot of the extent of reaction diverges in the critical region. According to the phase rule, the physical and chemical properties are isomorphic in the sense that in each case the critical behavior is determined by three fixed thermodynamic intensive variables.

The sandwiches of magnetic/nonmagnetic/magnetic (M/NM/M) materials have been investigated combined with Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange interactions with mixed apins-2 and 3/2 using Ising model using Monte Carlo simulations. The RKKY value is obtained for different distance between the different magnetic and non magnetic multilayer. The RKKY exchange interactions as a function of distance between the magnetic multilayer have been given. The magnetizations and magnetic susceptibilities of each magnetic bloc are obtained. The reduced critical temperatures of each bloc and the system are obtained. The reduced critical temperature is obtained for a fixed size. The theoretical calculations showed an oscillating behavior of the magnetic parameters with increasing the nonmagnetic layers. The total magnetization versus the exchange interactions and crystal field in each bloc is established. The magnetic hysteresis cycles are established for a fixed magnetic parameters.

Thermodynamic properties (isochoric heat capacity, critical and phase transition temperatures, pressure and thermal-pressure coefficient) of a nanofluid (2-propanol + TiO2) were experimentally studied near the critical point of the pure base fluid (2-propanol). Measurements were made using a high-temperature, high-pressure, nearly constant-volume adiabatic piezo-calorimeter that was designed for simultaneous measurements of caloric ( C V V T ) and density ( PVT ) properties of fluids along the near-critical isochores as a function of temperature in the two-phase and single-phase regions. The standard uncertainty of the density, temperature, pressure, thermal-pressure coefficient, and heat capacity measurements is estimated to be 0.1%, 0.02 K, 0.5%, 1.0%, and 1.5%, respectively. The measurements were made along a selected near-critical isochore of 282.68 kg·m−3 for a concentration of 0.132 mass fraction of TiO2 in the temperature range from (314 to 511) K. The measured C V and critical temperature data were interpreted in terms of finite-size scaling theory of critical phenomena for fluids confined in the finite-size media. The influence of finite size on the thermodynamic properties of the near- and supercritical fluid has been studied, along with thermal instability of the nanofluid (2-propanol + TiO2) at high temperatures (around 500 K).

A facility characterization test campaign was performed for NASA in SCIROCCO Plasma Wind Tunnel, with increasing enthalpy and constant reservoir pressure. In the frame of numerical rebuilding of the experimental data, an important gap among measured and numerically predicted values of heat flux led to deep analyse the numerical methods and the models usually employed for test rebuilding. The Navier–Stokes model with chemical reacting non-equilibrium flows, denoted a lack of physical accuracy due to local rarefaction effects, as certified by means of the continuum breakdown parameter. Furthermore, the low stagnation pressure environment could influence the surface catalytic behaviour of the hemisphere copper probe, and the chemical contribution to the stagnation heat flux. At the end, a set of direct simulation Monte Carlo with partial catalytic behaviour of the probe was performed, in order to address both critical phenomena highlighted and close the gap with the measured heat fluxes, understanding the actual test chamber environment.

In the probe limit, we investigate the effect of the quartic field strength correction to the usual Maxwell field on the holographic paramagnetism/ferromagnetism phase transition in the background of a 4-dimensional Schwarzschild-AdS black hole spacetime. We find that the presence of the higher correction parameter a to the Maxwell field decreases the critical temperature and makes the condensation harder to form in the case without external magnetic field. Furthermore, the increase of a will result in shortening the period of external magnetic field. Keywords: AdS/CFT correspondence, Holographic ferromagnetism, Maxwell field strength corrections

New experimental data on solubility and critical states in quaternary system propionic acid–ethanol–ethyl propionate–water at 293.15, 303.15 and 313.15 K and atmospheric pressure are presented. Solubility and critical (plait) points were obtained by “cloud-point technique” method. Experimental results on critical states in quaternary system at polythermal conditions (293.15–313.15 K) are presented as a critical surface in composition tetrahedron. The experimental data are compared with the results of calculations on the base of UNIFAC model.

We present an analytical solution of an effective field theory which, in one of its formulations, is equivalent to the Ginzburg’s Ψ -theory for the behavior of the Casimir force in a film of 4 He in equilibrium with its vapor near the superfluid transition point. We consider three versions of the theory, depending on the way one determines its parameters from the experimental measurements. We present exact results for the behavior of the order parameter profiles and of the Casimir force within this theory, which is characterized by d = 3 , ν = 2 ∕ 3 and β = 1 ∕ 3 , where d is the bulk spatial dimension and ν and β are the usual critical exponents. In addition, we revisit relevant experiments (Garcia and Chan, 1999) and (Ganshin et al., 2006) in terms of our findings. We find reasonably good agreement between our theoretical predictions and the experimental data. We demonstrate analytically that our calculated force is attractive. The position of the extremum is predicted to be at x min = π , with x = ( L ∕ ξ 0 ) ( T ∕ T λ − 1 ) 1 ∕ ν , which value effectively coincides with the experimental finding x min = 3 . 2 ± 0 . 18 . Here L is the thickness of the film, T λ is the bulk critical temperature and ξ 0 is the correlation length amplitude of the system for temperature T > T λ . The theoretically predicted position of the minimum does not depend on the one adjustable parameter, M , entering the theory. The situation is different with respect to the largest absolute value of the scaling function, which depends on both ξ 0 and on M . For this value the experiments yield − 1 . 30 . If one uses ξ 0 = 1 . 63 A , as in the original Ψ theory of Ginsburg, one obtains the closest approach to the experimental value − 1 . 848 with M = 0 . If one uses M = 0 . 5 , as inferred from other experiments, along with the best currently accepted experimental value for ξ 0 , ξ 0 = 1 . 432 A , then the maximum value of the force is predicted to be − 1 . 58 . The effective theory considered here is not consistent with critical point universality; furthermore it incorrectly predicts ordering in the film in violation of known rigorous results. These issues are discussed in the text.

It is well-known that the first-order phase transition (PT) will yield a stochastic gravitational waves (GWs) background with a logo-like spectrum. However, we show that when such a PT happened during the primordial inflation, the GWs spectrum brought by the PT will be reddened, which thus records the unique voiceprint of inflation. We assess the abilities of the GW detectors to detect the corresponding signal., 12 pages, 6 figures

In this contribution I will give an overview of the current activities worldwide to explore the phase structures of strongly interacting matter in the region of high baryochemical potential. After a review of the current and future high μB facilities I will briefly discuss the anticipated physics performance of several observables.

We study the subregion complexity in a semi-analytical holographic QCD model. Two cases with different warped factor are considered and both can realize confinement-deconfinement transition. By studying the behavior of the renormalized holographic complexity density $\hat{\cal C}$ versus the subregion length scale $\ell$, we find that for both cases, $\hat{\cal C}$ always experiences a discontinuity at certain critical value $\ell_c$ in confinement phases, while it is always continuous in deconfinement phases. This property may be seen as a signal to characterize confinement or deconfinement phases. The behavior of $\hat{\cal C}$ versus the temperature and chemical potential is also investigated and our results show that $\hat{\cal C}$ exhibits behavior characterizing the type of the transition. That is, it experiences a discontinuity at the transition temperature for $��< ��_c$ where first-order confinement-deconfinement phase transition happens, while it is always continuous for $��> ��_c$ where the transition turns into a turnover. These results imply that the renormalized holographic complexity density may be used as a good parameter to characterize the corresponding phase structures., v1:21 pages, 8 figures; v2:minor modifications, refs added. Publised version

This work was inspired by works of Gianfranco D’Anna (2000) where the Portevin-Le Chaˆtelier effect (PLC) was investigated by compressing Al-Mg alloy specimen in a very large deformation range and the results were interpreted from the viewpoint of phase transitions and critical phenomena. Two critical points where deformation process changes from “laminar” to jerky flow and back were noticed. We found that the second critical point where the rate of the serrations is decreased before the macroscopic fracture is not reachable for some alloys even with proposed geometry. We have tested 2 sets of specimens made of the same AMG6 alloy (~6% of magnesium) but with different amount of Si obtained from different producers. Specimens with a higher amount of Si tends to fracture before reaching the second point. Also, we have measured the amount of stored energy which can be recovered as heat during the annealing process. We used the differential scanning calorimeter STA "Jupiter" 449. We found that the amount of this energy sharply increases with the beginning of PLC serrations (first critical point) and drops at a second critical point or at macroscopic fracture. This can be related to a special type of critical phenomena—structural scaling transitions in mesodefect ensembles and associated structural relaxation mechanisms Naimark (2016)

In this present article, I primarily do research on the magnetic, magnetocaloric, and critical phenomena of the SrCoO3 perovskite. To study the aforesaid aspects of the system, I first start determining its transition temperature before establishing the second-order transition of the magnetic phase in the SrCoO3 perovskite by the positive slopes of the Arrott plot. Besides, I extract the values of the critical exponents β, γ and δ by employing the modified Arrott plot methods and the scale relation of Widom. In this way, the main research findings are: the transition temperature of the studied system is Tc=300K; beneath 5 T, the values of both the magnetic entropy change and the relative cooling power are 2.89 J /kg K and 189,17J/Kg, respectively; the results of critical phenomena indicated the presence of a long-range ferromagnetic order.

The complex magnetic nature of 5d layered iridate Sr2IrO4, owing to IrO6 octahedral rotation has triggered great interest in recent years. In this article, we investigated the magnetic excitations in layered canted antiferromagnet Sr2IrO4 via dc magnetization measurements and report the Griffiths phase (GP) signatures above the magnetic ordering temperature T N . The non-analytic nature of GP leads to unique critical exponent, β = 0.75(1) extracted from modified Arrott plot, in corroboration with magneto-caloric study. However, the analysis by Bray model in GP regime yields a reliable critical exponent value of β = 0.18(1), belonging to two-dimensional XYh4 universality class. The study also suggests a new picture of largely debated insulating nature of Sr2IrO4 in context of GP above T N .

In this paper, we propose a new model to investigate the spreading dynamic and critical phenomena on complex networks based on SIR model. Different from previous studies, we combine the effects of activity rate and infected rate on spreading process. Network nodes become active according to different probability correlated with its degree. Active infected nodes can interact all active susceptible neighbors, meanwhile, recover at a certain probability. By means of the mean-field equations, we find the basic reproductive number and critical threshold of spreading dynamic can be explained by the eigenvalues and eigenvectors of the correlation matrix. Furthermore, we utilize analytical and numerical simulations to explore the critical phenomenon and spreading dynamics of homogeneous and heterogeneous networks respectively. Our results indicate that both homogeneous networks and heterogeneous networks of the model exhibit a critical threshold consists of critical activity rate and infection rate in the spreading dynamic. The critical threshold of infection rate is increased by node activity, and node activity also shows a critical phenomenon given certain infection rate. Results validate that our model is a feasible and economical method to control spreading dynamics and promote further application of innovation diffusion, viral marketing in reality.

We present both analytical and numerical results for the behaviour of the Casimir force in a Ginzburg–Landau type model of a film of a simple fluid or binary liquid mixture in which the confining surfaces are strongly adsorbing but preferring different phases of the simple fluid, or different components of the mixture. Under such boundary conditions an interface is formed between the competing phases inside the system which are forced to coexist. We investigate the force as a function of the temperature and in the presence of an external ordering field and determine the (temperature-field) relief map of the force. We prove the existence of a single global maximum of the force and find its position and value. We find the asymptotic behaviour of the force when any of the scaling fields becomes large while the other one is negligible. Contrary to the case of symmetric boundary conditions we find, as expected, that the finite system does not possess a phase transition of its own for any finite values of the scaling variables corresponding to the temperature and the ordering field. We perform the study near the bulk critical temperature of the corresponding bulk system and find a perfect agreement with the finite-size scaling theory.

The Monte Carlo replica algorithm studies of phase transitions and critical phenomena of the layered triangular antiferromagnetic Ising model with intralayer next-nearest neighbor interactions reveal a second-order transition from ordered and disordered phases to paramagnetic phase. The character of phase transitions is analyzed using the histogram technique and Binder cumulant method. Static critical exponents for the heat capacity α , susceptibility γ , order parameter β , correlation radius ν , and the Fisher exponent η are computed by means of the finite-size scaling theory. The second nearest neighbor interactions are shown to fail to change the universality class of the critical behavior in the 3D Ising model on a layered triangular lattice.

An approximate analytical formulation for the quasi-static, normal, elastoplastic indentation of ductile materials is presented. Explicit equations are derived, which describe the geometrical profile of material piling up above the original surface in cases of spherical and conical indentation. Cases of rigid, elastic, and plastic indenters are modelled. Surface bulging in such cases is known to be related to stress concentration and increased risk of damage in the form of crack initiation, spalling, and generation of sizeable wear debris when the dented surface is loaded against another surface. The developed equations offer a simple and robust method to include such critical phenomena in damage models. A major part of the study is devoted to experimentally validating the developed equations in spherical and conical indentation. The related comparisons show satisfactory to excellent agreement with experimental results, even in cases of micro-indentation. The algorithm of the method is also provided for easy implementation of the method by the reader.

Benford's law is an empirical edict stating that the lower digits appear more often than higher ones as the first few significant digits in statistics of natural phenomena and mathematical tables. A marked proportion of such analyses is restricted to the first significant digit. We employ violation of Benford's law, up to the first four significant digits, for investigating magnetization and correlation data of paradigmatic quantum many-body systems to detect cooperative phenomena, focusing on the finite-size scaling exponents thereof. We find that for the transverse field quantum XY model, behavior of the very first significant digit of an observable, at an arbitrary point of the parameter space, is enough to capture the quantum phase transition in the model with a relatively high scaling exponent. A higher number of significant digits do not provide an appreciable further advantage, in particular, in terms of an increase in scaling exponents. Since the first significant digit of a physical quantity is relatively simple to obtain in experiments, the results have potential implications for laboratory observations in noisy environments., 7 pages, 1 figure, 1 table

The classification of homogeneous compact Einstein manifolds in dimension six is an open problem. We consider the remaining open case, namely left-invariant Einstein metrics g on G = SU ( 2 ) × SU ( 2 ) = S 3 × S 3 . Einstein metrics are critical points of the total scalar curvature functional for fixed volume. The scalar curvature S of a left-invariant metric g is constant and can be expressed as a rational function in the parameters determining the metric. The critical points of S , subject to the volume constraint, are given by the zero locus of a system of polynomials in the parameters. In general, however, the determination of the zero locus is apparently out of reach. Instead, we consider the case where the isotropy group K of g in the group of motions is non-trivial. When K ≇ Z 2 we prove that the Einstein metrics on G are given by (up to homothety) either the standard metric or the nearly Kahler metric, based on representation-theoretic arguments and computer algebra. For the remaining case K ≅ Z 2 we present partial results.

The magnetic ordering in Pr 2 Pt 2 In was investigated by means of magnetization and magnetic susceptibility measurements. The compound was found to order ferromagnetically at T C = 8.8(2) K with a second-order phase transition. The derived critical exponents β = 0.325(2), γ = 1.058(2) and δ = 4.26(4) are close to those expected for a 3D Ising ferromagnet.

The Landau–Ginzburg–Wilson Hamiltonian with random temperature for the phase transition in disordered systems from the Griffiths phase to ordered phase is reexamined. From the saddle point solutions, especially the excited state solutions, it is shown that the system self-organizes into blocks coupled with their neighbors like superspins, which are emergent variables. Taking the fluctuation around these saddle point solutions into account, we get an effective Hamiltonian, including the emergent superspins of the blocks, the fluctuation around the saddle point solutions, and their couplings. Applying Stratonovich–Hubbard transformation to the part of superspins, we get a Landau–Ginzburg–Wilson Hamiltonian for the blocks. From the saddle point equations for the blocks, we can get the second generation blocks, of which sizes are much larger than the first generation blocks. Repeating this procedure again and again, we get many generations of blocks to describe the asymptotic behavior. If a field is applied, the effective field on the superspins is multiplied greatly and proportional to the block size. For a very small field, the effective field on the higher generation superspins can be so strong to cause the superspins polarized radically. This can explain the extra large critical isotherm exponent discovered in the experiments. The phase space of reduced temperature vs. field is divided into many layers , in which different generation blocks dominate the critical behavior. The sizes of the different generation emergent blocks are new relevant length scales. This can explain a lot of puzzles in the experiments and the Monte Carlo simulation.

A comprehensive analysis of the critical phenomena for the nominal compositions La 0.8 Na 0.2 Mn 1-x Bi x O 3 (0 ≤ x ≤ 0.06) was carried out. The critical exponents values were calculated by various techniques such as Modified Arrott plot (MAP), Kouvel Fisher (KF) method and critical isotherm (CI). Comparison of the experimental data with the above theoretical models showed that the critical exponents β, γ and δ for the undoped sample are quite well described by the tricritical mean-field model (TMF). Furthermore, the substitution of Mn by Bi ions led to the increase of γ which approached the 3D-Heisenberg model (γ = 1 325 and β took similar values to those predicted by the TMF model. The validity of the exponents values was confirmed with the scaling hypothesis; the M (T, e) curves collapse onto two independent universal branches below and above Tc.

We present an analytical solution for the connectivity of a network model with a "non-simultaneous" linking scheme. Despite its simplicity, this model exhibits node-space correlations in the link distribution, and anomalous fluctuations behavior of the time series of the connectivity variable, and a finite-size e ff ect: the maximum number of links occurs away from the critical value of the system parameter. We derive an exact Master Equation for this model using a quantum algebra approach to stochastic processes. Fluctuations are much more important than the mean-field approximation predicts, which we attribute to the heterogeneity in the model. The maximal heterogeneous population corresponds to the critical value of the system. Finally as an explanatory case we evaluate the growth of the network value in relation with the system interconnectedness.

Magnetic and magnetocaloric properties, as well as the phase diagrams of a ferromagnetic ternary alloy system have been studied. A detailed comparison of two different methods, namely the effective field theory (EFT), and Monte Carlo (MC) simulations has been provided. Our numerical data show that the general qualitative picture presented by two methods are in a good agreement with each other. In terms of the magnetocaloric properties, our results yield that it is possible to design magnetic materials with a variety of working temperatures and magnetocaloric properties (such as large Delta S-M and q values) by manipulating the magnetic phase transition via tuning the compositional factor (i.e. the mixing ratio of sublattice ions). The observed magnetocaloric effect has been found to be a direct one with Delta S-M < 0 associated with a second order phase transition.

We discuss experimentally and theoretically neutron production from the laser driven explosion of gas clusters prepared near the liquid-gas critical point. We let deuterated methane that was prepared very close to its critical temperature and pressure expand through a conical nozzle to create clusters, and then irradiated those clusters with a high intensity pulse from the Texas Petawatt Laser. After ionization, the clusters explode producing energetic ions, some of which fuse with resultant neutron emission. We show that the critical fluctuations present in the nozzle before the expansion influence the dynamics of neutron production. Neutron production near the critical point follows a power law, which is a signature of a second order phase transition and it is consistent with the Fisher model. This result might be relevant for energy production from fusion reactions.

The spin-glass (SG) behavior, magnetocaloric effect, and critical behavior of MnCr2O4 were investigated using dc/ac magnetic measurements. The strong magnetic anisotropy is observed from the dc magnetizations. The peaks of ac susceptibility display dependence on the frequency and magnetic field. Meanwhile, magnetic relaxation measurements show a slow decay of the remanent magnetization with time. These findings consistently demonstrate the coexistence of the SG component and long-range ferrimagnetic (FIM) order in MnCr2O4. The SG at low temperature is not conventional but has a reentrant character. Importantly, the reentrant SG (RSG) behavior in MnCr2O4 originates from the freezing and fluctuation of the short-range spiral order at low temperatures. On the other hand, the magnetocaloric effect (MCE) in spinel compounds MnCr2O4 was reported in this study. According to the isotherms measurements, the magnetic entropy change | Δ S M | = 6.1 J kg−1 K−1 was calculated under applied field H = 50 kOe. A comprehensive study of the critical behavior of MnCr2O4 near the paramagnetic (PM) to FIM transition, might be helpful in understanding the interesting magnetic interaction of MnCr2O4. Besides, the critical exponents of MnCr2O4 was obtained [β = 0.488 and γ = 0.918 for MAP, β = 0.473 and γ = 0.909 for KF] by the different theoretical models. Interestingly, it is found that the critical phenomena of MnCr2O4 are close to the mean-field model.

In this paper, we study quantum phase transitions (QPTs) and critical phenomena of the one-dimensional Ising-Gamma model, which describes the competition between the Ising interactions and the off-diagonal Gamma exchange interactions. The Hamiltonian is analytically solved in virtue of Jordan–Wigner, Fourier and Bogoliubov transformations. The phase diagram consists of three phases, including antiferromagnetic phase, paramagnetic phase and gapless spiral phase. A detailed study of information measures including the Wigner–Yanase skew information (WYSI) and quantum fidelity susceptibility (QFS) is conducted. The second-order QPTs are witnessed both by WYSI and QFS. When the QPT occurs between distinct gapped phases, a logarithmic scaling behavior of local measures and a superextensive behavior of fidelity susceptibility are identified, while they exhibit size-dependent behaviors for the gapped-to-gapless transitions. The correlation-length exponent extracted from various order parameters agrees well with each other.

We consider a generalized version of the majority-vote model in small-world networks. In our model, each site of the network has noise q = 0 and q ≠ 0 with probability f and 1 − f , respectively. The connections of the two-dimensional square lattice are rewired with probability p . We performed Monte Carlo simulations to characterize the order–disorder phase transition of the system. Through finite-size scaling analysis, we calculated the critical noise value q c and the standard critical exponents β ∕ ν , γ ∕ ν , 1 ∕ ν . Our results suggest that these exponents are different from those of the isotropic majority-vote model. We concluded that the zero noise fraction f when combined with the rewiring probability p drive the system to a different universality class from that of the isotropic majority-vote model.

Near the paramagnetic to ferrimagnetic transition temperature, the dc magnetization data of two sulpho spinels, CoCr2S4 and FeCr2S4, are analyzed by the modified Arrott plot, the Kouvel-Fisher method, log M vs log H, and the scaling analysis. Critical exponents β = 0.3946 ± 0.0064, 0.421 ± 0.04, γ = 1.101 ± 0.004, 1.041 ± 0.015, and δ = 3.77 ± 0.06, 3.512 ± 0.14 are obtained around the critical temperature ∼ 224.4 K and 166.5 K for CoCr2S4 and FeCr2S4, respectively. Scaling analysis indicates that calculated critical exponents, as well as critical temperatures, are intrinsic to the systems. The values of critical exponents of CoCr2S4 are between those predicted for a three dimensional Heisenberg model and those predicted by mean field theory. Probably, the observed large spin-phonon coupling and magnetocrystalline anisotropy caused by Co ion may play the key role in this critical behavior of CoCr2S4. The critical exponents of FeCr2S4 are close to the mean field theory except for δ, which is higher than the theoretical value. The higher value of δ may arise due to the incomplete ferrimagnetic transition and presence of short range magnetic ordering above T C for FeCr2S4.

We study the phase transition in a discrete opinion dynamics model on an Apollonian network, where mutual interactions can be both positive and negative depending on the noise parameter q . We have characterized the critical exponents of the phase transitions through the Monte Carlo simulations and finite-size scaling analysis. Our finds attest that different from the equilibrium models, such as Ising and Potts on Apollonian network that do not present phase transition, the kinetic model report does. Moreover, we have included one additional aspect on the Apollonian network, the effect of redirecting a fraction of p of the network’s links. On this redirected network, we obtained the exponents ratio β ∕ ν , γ ∕ ν , and 1 ∕ ν for several values of rewiring probability p . Similar to this model’s results on free-scale networks, the effective dimensionality of the system found was D e f f ≈ 1 . 0 for all values of p . The results presented here demonstrate that kinetic models of discrete opinion dynamics belong to a different universality class as the equilibrium Ising Model on Apollonian networks. It is noticed that the kinetic model study here and the majority-vote model on Apollonian networks are in the same universality class, for a rewiring probability lower than 0.5. Above p = 0 . 5 , the critical exponents are different from those found in the majority-vote model on Apollonian networks.

This article is a review and at the same time contains a number of original ideas and results that allow formulating the principal reason for the hexagon formation in systems of animate and inanimate nature. The main goal of this study lies in the application of synergetic methods at the border of physics and medicine. More precisely, a synergetic analogy is considered between two systems of absolutely different nature in which hexagonal structures arise, namely: (a) the physical system of Benard cells and (b) the neurophysiological system of grid cells in the brain (Nobel Prize in physiology or medicine in 2014, which was awarded to J.O'Keefe, E.I.Moser, and M.-B.Moser). To explain the principal reason of the hexagon formation in the brain, “Feynman's classification of three stages in studying natural phenomena” is proposed to use, especially the 3rd stage of studying, associated with the understanding first principles underlying these phenomena. On the basis of the proposed fluctuation model, in which the Ginzburg-Landau Hamiltonian, the Polyakov hypothesis of conformal invariance, and Haken results on Benard cells are used, the first principle for the hexagon formation in system of grid cells is formulated as a manifestation of the nonlinear interaction of order-parameter fluctuations. The vertices of the virtual hexagon in 6-grid lattice represent the geometric place of those points at which the interaction of fluctuations is realized and the action potential (AP), i.e. a so-called “firing of AP”, appears in neurons. In accordance with the universality hypothesis and synergetic similarity of hexagon formation in systems of Benard and grid cells, these both systems should belong to the same universality class of the 3-dimensional Ising model having a scalar order parameter. This class of universality includes classic liquids and liquid mixtures, liquid crystals in the Maier-Saupe approximation, chemically reacting system of grid cells in the brain and other systems. Another goal of the article is to attract the attention of researchers (not only physicists, chemists and mathematicians, but also neurophysiologists, biologists and physicians) to the problem of structure formation in living and inanimate world, using ideas of the fluctuation theory of phase transitions and critical phenomena, statistical thermodynamics, universality classes, scaling and conformal invariance hypotheses.

The phase-transformation-like behavior of grain boundaries, where their chemistry, structure and properties change discontinuously, is emerging as a fundamental interest in the context of grain boundary engineering. The cases studied so far pertain primarily to elemental metals and dilute alloy systems. The next step of complexity would be a system still of a single phase structure but involving multiple and concentrated elements. The recently emerging high/medium entropy alloys (H/MEAs), alternatively known as complex concentration alloys (CCAs), fit the bill in this regard. Here we use CoCrNi as a model CCA to highlight that intricate interatomic interactions influence the grain boundary element distribution and consequently phase transitions. By combining classical molecular dynamics simulations and first-principles density functional theory calculations, we reveal that grain boundary phase transition temperature is sensitive to the grain boundary atomic configuration. The CCA grain boundary with random atomic distribution is more apt to transform due to a larger thermodynamic driving force and faster diffusion kinetics, compared to a hypothetical reference that bears the same bulk properties but no distinguishable constituent components. In contrast, when the three elements redistribute with local Ni-clustering and Co–Cr ordering in the grain boundary structure, diffusion is rendered more sluggish, delaying grain boundary phase transformation. Our work is a step forward in understanding critical phenomena in grain boundaries and CCAs, and enriches the knowledge base for materials design via grain boundary engineering.

At criticality in two dimensions, the size distribution of holes within a large percolation cluster or backbone was recently found to be governed by a power law with the exponent given by a hyperscaling relation. It was also found that, though the boundary of the largest hole is a fractal, the size of the largest hole itself is proportional to L d , where L represents the linear system size and d = 2 is the spatial dimension. In this work, we study the probability distribution of the size of the largest hole in the largest percolation cluster and that in the largest backbone, and compare them with the probability distribution of the size of the largest percolation cluster and that of the largest backbone themselves. We obtain these four size distributions in the critical region by Monte Carlo simulations for the two-dimensional bond percolation model on the square lattice with periodic boundary conditions. It is found that each of these distributions can be described by a different single-variable function P ( C , L ) d C = P ( x ) d x , with x ≡ C ∕ L d C , where C is the size of the structure whose (fractal) dimension is d C . The function P ( x ) is generally not unimodal, and interestingly, for the largest cluster hole, symmetric properties are found in its size distribution due to duality, e.g., P ( x ) is symmetric around the mean value x = 1 at the percolation threshold p c . We characterize these size distributions by calculating the variance and different dimensionless cumulant ratios, which exhibit rich critical behaviors at the pseudocritical and critical points. For example, the extremum of the excess kurtosis and the zero point of the skewness locate at the same (pseudocritical) point, whose values are different for the four structures but approach p c in the limit L → ∞ . We also perform wrapping analyses for each size distribution, showing that different wrapping types contribute to the overall distribution in different forms.

The exact solution of ferromagnetic two-dimensional (2D) Ising model with a transverse field, which can be used to describe the critical phenomena in low-dimensional quantum spin systems, is derived by equivalence between the ferromagnetic 2D Ising model with a transverse field and the ferromagnetic three-dimensional (3D) Ising model. The results obtained in this work can be extended to be suitable for the antiferromagnetic 2D Ising model with a transverse field in the cases without frustration.

The Monte Carlo method has been used to study the magnetic and thermodynamic properties of a hexagonal ferrimagnetic Ising nanoparticle with spin-3/2 inner core surrounded by spin-1 surface shell layers. The effects of exchange couplings and crystal-fields on the compensation behaviors and critical phenomena of the system have been investigated in detail. Many types of the magnetization curves have been found, depending on the competitions among the exchange couplings, the crystal-fields and the temperature. The phase diagrams for different exchange couplings and crystal-fields have been also obtained. In Particular, we have discovered the double and triple hysteresis loops for certain physical parameters in the present system. An excellent agreement has been achieved from the comparison between our results and the previous studies.

Magnetocaloric effect (MCE) in multiferroic cubic spinel MnCr2O4 (space group Fd (3) over barm, no. 227, cF56), has been investigated using dc magnetization studies. The values of maximum magnetic entropy change (Delta S-M(max)) and the adiabatic temperature change (Delta T-ad) are similar to 5.3 J kg(-1) K-1 and similar to 2 K, respectively, at similar to 42.8 K for the magnetic field change of 50 kOe. The dc magnetization data near the transition temperature were analyzed by the modified Arrott plots, the Kouvel-Fisher method, log M vs log H, and the scaling analysis. Critical exponents beta = 0.3932 +/- 0.0287, gamma = 1.0256 +/- 0.0239, and delta = 3.55 +/- 0.26 are obtained around the critical temperature similar to 42.88 K. The critical exponents are in excellent agreement with the single scaling equation of state M(H, is an element of) = is an element of(0: 3932 +/- 0: 0287) f(+/-)(H/is an element of(((0: 3932 +/- 0: 0287)+(1: 0256 +/- 0: 0239)))); with f(+) for T > 42.88 K, f(-) for T < 42.88 K, and is an element of = (T - 42.88)/42.88. At T = 42.88 K, the exponent d relates the magnetization with applied filed by M - H-(1/3: 55 +/- 0: 26) Scaling analysis shows that calculated critical exponents as well as critical temperature are intrinsic to the system. Theoretically, the value of b is close to 3D Heisenberg model, while values of c and d are close to those of the mean field model. So the values of critical exponents indicate that the critical behavior of MnCr2O4 cannot be described within the framework of existing universality classes and probably belong to a separate class. (C) 2017 Elsevier B.V. All rights reserved.

We investigate a Born--Infeld-type model of nonlinear electrodynamics, possessing three parameters, coupled with general relativity. As a particular case Born--Infeld electrodynamics is reproduced. There is no singularity of the electric field at the centre of point-like charged particles and self-energy of charges is finite in this model. The magnetized black hole is studied and solutions are obtained. We demonstrate that for some parameters of the model the black hole is regular. We find the asymptotic of the metric and mass functions at $r\rightarrow\infty$ and $r\rightarrow 0$, and corrections to the Reissner--Nordstr\"{o}m solution. Thermodynamics of black holes is investigated. We calculate the Hawking temperature of black holes and show that black holes are not stable and there are phase transitions in the model under consideration., Comment: 15 pages, 6 figures, corrected Eq. (26) and Fig. 6

PρTx relationship of the binary 1-propanol + n -hexane mixture were measured. Measurements were concentrated in the immediate vicinity of the critical and supercritical regions in order to closely observe the features of the mixture critical curve behavior (critical phenomena in the 1-propanol + n -hexane mixture) and other derived thermodynamic properties. The measurements have been made over the temperature range from (403 to 573) K for liquid and vapor isochores between (92 and 564) kg·m − 3 up to 61 MPa using a high-temperature and high-pressure constant-volume piezometer. The combined expanded uncertainty of the density, ρ , pressure, P , temperature, T , and concentration, x , measurements at the 95% confidence level with a coverage factor of k = 2 is estimated to be 0.15%, (0.02 to 0.05) %, 10 mK, and 0.01 mole %, respectively. The critical curve data ( T C − x ), ( P C − x ), and ( ρ C − x ), were extracted from the measured PρTx data. The extracted critical curve and direct measured P − x data along the critical isochore-isotherm were used to estimate the value of the Krichevskii parameter for the mixture when 1-propanol is solvent at the critical state. The measured PρTx data were used to calculate excess and partial molar volumes of n -hexane near the critical point of pure 1-propanol. The isomorphic thermodynamic behavior of the mixture have been studied on the bases of critical curve data and the critical amplitudes of the pure solvent (1-propanol).

Asymptotic properties of the symmetric and asymmetric naming games have been studied under some restrictions in a community of agents. In one version, the vocabulary sizes of the agents are restricted to finite capacities. In this case, compared to the original naming games, the dynamics takes much longer time for achieving the consensus. In the second version, the symmetric game starts with a limited number of distinct names distributed among the agents. Three different quantities are measured for a quantitative comparison, namely, the maximum value of the total number of names in the community, the time at which the community attains the maximal number of names, and the global convergence time. Using an extensive numerical study, the entire set of three power law exponents characterizing these quantities are estimated for both the versions which are observed to be distinctly different from their counter parts of the original naming games.

The quantum phase transition and thermodynamics of a periodic Anderson-like polymer chain in a magnetic field are investigated by Green’s function theory. The T - h phase diagram is explored, wherein a crossover temperature T ∗ denoting the gapless phase crossover into quantum critical regimes, smoothly connects near the critical fields to the universal linear line T ∗ ∼ ( h − h c,s ), and ends at h c,s , providing a new route to capture quantum critical point (QCP). The quantum critical scaling around QCPs is demonstrated by analyzing magnetization, specific heat and Gruneisen parameter Γ h , which provide direct access to distill the power-law critical exponents ( β , δ and α ) obeying the critical scaling relation α + β (1 + δ ) = 2, analogous to the quantum spin system. Furthermore, scaling hypothesis equations are proposed to check the scaling analysis, for which all the data collapse onto a single curve or two independent branches for the plot against an appropriate scaling variable, indicating the self-consistency and reliability of the obtained critical exponents.

The equation of state of the SU($3$) Yang-Mills theory is determined in the deconfined phase with a precision of about 0.5%. The calculation is carried out by numerical simulations of lattice gauge theory with shifted boundary conditions in the time direction. At each given temperature, up to $230\, T_c$ with $T_c$ being the critical temperature, the entropy density is computed at several lattice spacings so to be able to extrapolate the results to the continuum limit with confidence. Taken at face value, above a few $T_c$ the results exhibit a striking linear behaviour in $\ln(T/T_c)^{-1}$ over almost 2 orders of magnitude. Within errors, data point straight to the Stefan-Boltzmann value but with a slope grossly different from the leading-order perturbative prediction. The pressure is determined by integrating the entropy in the temperature, while the energy density is extracted from $T s=(\epsilon + p )$. The continuum values of the potentials are well represented by Pad\'e interpolating formulas, which also connect them well to the Stefan-Boltzmann values in the infinite temperature limit. The pressure, the energy and the entropy densities are compared with results in the literature. The discrepancy among previous computations near $T_c$ is analyzed and resolved thanks to the high precision achieved., Comment: 7 pages, 3 figures. A few sentences and one reference added

We assess currently available experimental data of the diameter of the coexistence curve for the gas–liquid phase transition of pure fluids. Various approaches, including the direct evaluation of dielectric-constant data and the analysis of calorimetric experiments, are found to support a leading | T - T c | 2 β singular term in the diameter, with β ≅ 0.326 and Tc the critical temperature. This is consistent with the predictions from “complete scaling” formulation of asymmetric fluid criticality.

The PVTx properties of binary (1-propanol + n -pentane) mixture have been measured over wide temperature and pressure ranges from (306.15 to 573.15) K for densities between (15.52 and 663.69) kg·m −3 up to 49.09 MPa for four concentrations (0.2, 0.5, 0.8, and 0.9 mol fraction of n -pentane). The well-known high-temperature and high-pressure constant-volume piezometer technique was used for measurements of the PVTx relationship. The measurements were concentrated in the critical and supercritical regions in order to study the features of the mixture critical curve behaviour (critical phenomena in the (1-propanol + n -pentane) mixture and other derived thermodynamic properties near the liquid-gas critical points. The combined expanded uncertainty of the density ( ρ ), pressure ( P ), temperature ( T ), and concentration ( x ), measurements at the 95% confidence level with a coverage factor of k = 2 is estimated to be 0.2% (density in the liquid phase), 0.3% (density in the gas phase); 0.5% (density in the critical and supercritical regions); 0.05% (pressure), 15 mK, and 0.01 mol%. The critical curve values ( T C - x ), ( P C - x ), and ( ρ C - x ), were determined from the measured PVTx results. The value of the Krichevskii parameter ( ∂ P / ∂ x ) T C V C ∞ = 7.985 MPa for (1-propanol + n -pentane) mixture was estimated from the present and reported critical curve and the directly measured P - x results along the critical isochore-isotherm of pure 1-propanol. The critical curve values were also used to study the critical phenomena (isomorphism in the binary mixture) in the (1-propanol + n -pentane) mixture. In particular, the characteristic reduced temperature and density differences, which determine the isomorphic thermodynamic behaviour (pure-like and mixture-like critical behaviour) of the mixture, were estimated using the critical curve values. The measured PVTx values were also used to calculate the derived volumetric properties such as excess and partial molar volumes of n -pentane near the critical point of pure 1-propanol.

We analytically obtain a new charged Lifshtitz solution by adding a non-relativistic Maxwell field in Horava-Lifshitz gravity. The black hole exhibits an anisotropic scaling between space and time (Lifshitz scaling) in the UV limit, while in the IR limit, the Lorentz invariance is recovered. We introduce the probed Lorentz-violation fermions into the background and holographically investigate the spectral properties of the dual fermionic operator. The Lorentz-violation of fermions will enhance the peak and corresponds larger fermi momentum, which compensates the non-relativistic bulk effect of the dynamical exponent. For a fixed $z$, when the Lorentz-violation of fermions increases to a critical value, the behavior of the low energy excitation goes from a non-Fermi liquid type to a fermi liquid type, which implies a kind of phase transition., Comment: minor revisions, references added, published version

We communicate three formulas for the permanents of degenerate Schur and circulant matrices. These combinatorial and integral formulas are intended for the analytical and asymptotic evaluation of the permanents as well as for the solution of three-dimensional Ising model. The paper's goal is to draw attention to the open fundamental problem of finding the permanents' asymptotics. A solution to this problem would be tremendously important for physics of many-body systems and critical phenomena, as well as for quantum field theory.

We numerically investigate the holographic paramagnetism–ferromagnetism phase transition in the 4-dimensional Lifshitz spacetime in the presence of three kinds of typical Born–Infeld-like nonlinear electrodynamics. Concretely, in the probe limit, we thoroughly discuss the effects of the nonlinear parameter b and the dynamical exponent z on the critical temperature, magnetic moment and hysteresis loop. The results show that the exponential form of nonlinear electrodynamics correction makes the critical temperature smaller and the magnetic moment harder to form with the absent external field for a constant nonlinear parameter b comparing it with the logarithmic form of nonlinear electrodynamics and the Born–Infeld nonlinear electrodynamics, especially for the case of larger dynamical exponent z. Moreover, the increase of nonlinear parameter b (for the fixed z) or dynamical exponent z (for the fixed b) will result in extending the period of the external magnetic field. Particularly, the effect of the exponential form of nonlinear electrodynamics on the periodicity of hysteresis loop is more noteworthy.

We study holographic superconductor model with two scalar fields coupled to one single Maxwell field in the AdS soliton background away from the probe limit. We disclose properties of phase transitions mostly from the holographic topological entanglement entropy approach. With different sets of parameters, we observe various types of transitions, especially a new first order phase transition between the condensation of different order parameters in the insulator/superconductor system. Our results show that the entanglement entropy is a good probe to critical phase transition points and the order of phase transitions in the two-order model. We also conclude that the entanglement entropy is useful to some extent in determining the physically supported phases. In addition, we investigate properties of the condensation through the scalar operator and the charge density in the dual theory. As a summary, we draw the complete phase diagram of the effects of the scalar charge on phase transitions. At last, we give some qualitative understanding and obtain the analytical condition for the first order phase transition to occur., Comment: 12 pages, 7 figures. arXiv admin note: text overlap with arXiv:1512.08950

Fluctuation conductivity is experimentally studied in the genuine critical region near the superconducting transition of YBa 2 Cu 3 O 7 − δ , YBa 2 Cu 2.985 Fe 0.015 O 7 − δ and Y 0.95 Ca 0.05 Ba 2 Cu 3 O 7 − δ single crystal samples. Two fluctuation regimes where the electrical conductivity diverges as a power-law of the reduced temperature were systematically observed. In the first regime, farther from the critical temperature T c , the transition behaves as predicted by the thermodynamics of the three dimensional-XY (3D-XY) universality class characteristic of a second-order phase transition. In the asymptotic regime closer to T c a power-law regime characterized by a much smaller exponent is observed. The smallest value ever reported for the fluctuation conductivity exponent in the high- T c superconductors is obtained for the Fe- and Ca-doped systems. We suggest that the regime beyond 3D-XY is a crossover towards a weakly first-order transition induced by internal magnetic excitations.