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Constant-rate inflation, including ultra-slow-roll as a special case, has been widely applied to the formation of primordial black holes with significant deviation from the standard slow-roll conditions at both the growing and decaying phases of the power spectrum. We derive analytic solutions for the curvature perturbations with respect to the late-time scaling dimensions (conformal weights) constrained by the dilatation symmetry of the de Sitter background and show that the continuity of conformal weights across different rolling phases is protected by the adiabatic condition of the inflaton perturbation. The temporal excitation of subleading states (with the next-to-lowest conformal weights), recorded as the "steepest growth" of the power spectrum, is triggered by the entropy production in the transition from slow-roll to constant-rate phases., Comment: 18 + 4 pages, 6 figures; v2: references added, provided entropy production as a criterion for the steepest growth; v3: minor corrections, version matched with publication

We investigate how entanglement entropy behaves in a non-conformal scalar field system with a quantum phase transition, by the replica method. We study the $\sigma$-model in 3+1 dimensions which is $O(N)$ symmetric as the mass squared parameter $\mu^{2}$ is positive, and undergoes spontaneous symmetry breaking while $\mu^{2}$ becomes negative. The area law leading divergence of the entanglement entropy is preserved in both of the symmetric and the broken phases. The spontaneous symmetry breaking changes the subleading divergence from log to log squared, due to the cubic interaction on the cone. At the leading order of the coupling constant expansion, the entanglement entropy reaches a cusped maximum at the quantum phase transition point $\mu^{2}=0$, and decreases while $\mu^{2}$ is tuned away from 0 into either phase., Comment: 36 pp., 5 figures

Seismic anisotropy, wave attenuation, and dispersion are critical phenomena of wave propagation in real media. Full-wavefield modeling of wave behavior in such media plays an important role in investigating dynamic features of the earth’s interior and in full-waveform inversion of anisotropic parameters and velocity dispersion. We have developed a numerical scheme to model the full-waveform response from a point source in a vertically varying viscoelastic medium of arbitrary anisotropy. The method is implemented in the frequency domain, so the complexity of anelasticity and anisotropy can be described by a complex elastic stiffness matrix and frequency-dependent moduli can also be readily incorporated. In our scheme, we solve the elastodynamic equations for general anisotropy through finite-element method in the frequency-wavenumber domain and we use the stiffness reduction method to suppress reflections from artificial boundaries along the depth direction. A nonuniform 2D Fourier transform strategy is developed to reconstruct the spatial-domain counterparts from the wavenumber-domain solutions. The time-domain responses are then obtained by taking inverse fast Fourier transform with respect to frequency. We validate the method by comparing the numerical results with the exact solutions for a homogeneous transversely isotropic model and a two-layered model. In the application example, we further proved the feasibility and generality of the scheme using an attenuative, dispersive model with velocity and attenuation anisotropy. Our scheme enjoys significant advantages in incorporating various viscoelastic/dispersive behaviors and general anisotropy, and thus provides a useful tool for numerical simulation of dynamic responses in practical application.

Out of equilibrium, the lack of reciprocity is the rule rather than the exception. Non-reciprocal interactions occur, for instance, in networks of neurons, directional growth of interfaces, and synthetic active materials. While wave propagation in non-reciprocal media has recently been under intense study, less is known about the consequences of non-reciprocity on the collective behavior of many-body systems. Here, we show that non-reciprocity leads to time-dependent phases where spontaneously broken symmetries are dynamically restored. The resulting phase transitions are controlled by spectral singularities called exceptional points. We describe the emergence of these phases using insights from bifurcation theory and non-Hermitian quantum mechanics. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these non-reciprocal systems range from active time-(quasi)crystals to exceptional-point enforced pattern-formation and hysteresis. Our work paves the way towards a general theory of critical phenomena in non-reciprocal matter., Comment: Supplementary movies at https://home.uchicago.edu/~vitelli/videos.html

In the classically unbroken phase, 3d $O(N)$ symmetric $\phi^4$ vector models admit two equivalent descriptions connected by a strong-weak duality closely related to the one found by Chang and Magruder long ago. We determine the exact analytic renormalization dependence of the critical couplings in the weak and strong branches as a function of the renormalization scheme (parametrized by $\kappa$) and for any $N$. It is shown that for $\kappa=\kappa_*$ the two fixed points merge and then, for $\kappa, Comment: 38 pages, 12 figures; v3: version to appear in JHEP

Quantum phase transitions (QPTs) are usually associated with many-body systems with large degrees of freedom approaching the thermodynamic limit. In such systems, the many-body ground state shows abrupt changes at zero temperature when the control parameter of the Hamiltonian is scanned across a quantum critical point. Recently it has been realized that a QPT can also occur in a simple system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report the first experimental demonstration of a QPT in the QRM using a single trapped ion. We measure the average spin-up state population of the ion and the average phonon number in its spatial oscillation mode as two order parameters and observe the clear evidences of the phase transition via slow quench of the coupling between the ion and its spatial motion. An experimental probe of the phase transitions in a fundamental quantum optics model without imposing the thermodynamic limit opens up a new window for the controlled study of QPTs and quantum critical phenomena., Comment: 15 pages, 9 figures

The quantitative characteristics of the products of dispersion and the cascade of dissipative structures arising in metals under shock-wave loading are determined. The fractal dimension df and the Hurst exponent H (standardized range of dissipative structures) of the cascade of hydrodynamic modes, the roughness of the fracture surface, and the dispersion products are determined. Destructive processes occurring in loaded samples are numerically simulated using the Lagrangian technique TIM 3D [1, 2]. It is shown that a cascade of dissipative structures at different scale–temporal levels (nanolevel, mesolevel I, mesolevel II, and macrolevel) is a fractal cluster, and it is a percolation cluster on the threshold of a macrofracture, when there is connectivity in the system of dissipative structures [1, 2]. The self-similarity of dissipative structures is due to the self-organization in nonequilibrium systems; and the dynamic fracture and dispersion processes are examples of scale invariance. The scale invariance of the dissipative structures indicates the nonequilibrium system has reached a critical state.

Various critical phenomena and critical points appearing in many-particle systems under the variation of external conditions (fields), including the temperature, pressure, and magnetic and electric fields are described. Laws of statistical physics are universal for any particular nature of particles and the considered phenomena can be observed in systems of macroparticles (colloids), atoms, molecules, and subnuclear particles (nucleons and quarks).

The phase equilibria and critical phenomena in the Na2SO4–Na2B4O7–H2O system with the boundary subsystems Na2B4O7–H2O (type 1 with the phase separation of the solutions) and Na2SO4–H2O (type 2) at 350–460°C and a pressure of up to 100 MPa are studied. It is shown that there exist two three-phase regions L1–L2–S, which are adjacent to two water–salt subsystems and divided by a fluid region, at temperatures ranging from 440°C (the critical point Q (L1 = L2–S) of the type 2 binary system) to ~455°C (at which these regions unite). The ternary system has two critical curves in saturated solutions. The curves originate from different critical points of the type 2 binary subsystem, point p (G = L–S) and point Q (G = L1–L2–S), respectively, and end at the end ternary critical points pR (G = L1–L2–S) and QN (G–L1 = L2–S), respectively. Between the last two points, there is a four-phase equilibrium (G–L1–L2–S), which, according to the visual observations in the sealed quartz ampules, exists in the temperature range 350–380°C.

This review presents the results of a detailed analysis of the role of isochoric heat capacity as a key thermodynamic property of matter in the investigation of critical and supercritical phenomena. A brief historical background is given on the role and contribution of Russian scientific schools to the experimental investigation of the isochoric heat capacity in the critical region in the development of the nonclassical (scaling) theory of critical phenomena, which drastically changed the understanding of the physical nature of critical and supercritical phenomena. The experimental behavior of the isochoric heat capacity and other thermodynamic properties of fluids in the critical and supercritical regions related to it is investigated in detail. The role of new experimental studies of two-phase isochoric heat capacity near the critical point in the development of a “complete” scaling theory is discussed. This theory allows us to understand the physical nature of the asymmetry of the liquid–gas coexistence curve near the critical point and to estimate the contribution of the chemical potential to the divergence of the two-phase isochoric heat capacity at the critical point. The review also focuses on supercritical phase transitions and the role of isochoric heat capacity in determining the Widom line, which separates the liquid-like and gas-like regions in supercritical states; i.e., it defines the boundaries of the coexistence of liquid-like and gas-like phases in supercritical fluids.

We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal invariance of correlation functions, and imposes some relations between correlation functions of different orders. Numerical analysis shows that these conditions are incompatible unless the critical exponents take particular values, or more precisely that they must belong to a small island in the parameter space., Comment: 16 pages, 3 figures, accepted for publication by C.R.Physique

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.

In this review, we mention about the theoretical achievement of physics of surface Andreev bound state (SABS) and odd-frequency pairing during this quarter century based on our research. Currently, topological superconductors with Majorana edge state have become a central issue in condensed matter physics. It is noted that Majorana edge state is nothing but a zero energy surface Andreev bound state (ZESABS) and the study of ZESABS has started in the context of the pairing symmetry of high Tc cuprate. We mention our obtained conductance formula of quasiparticle tunneling and Josephson current in unconventional superconductor junctions through ZESABS have already captured the essence of the charge transport profile via the Majorana fermion. We also mention that in the presence of ZESABS, odd-frequency pairing like spin-triplet s-wave or spin-singlet p-wave is hugely enhanced near the surface or interface. We further analyze the spectroscopy of the induced odd-frequency pairings by extending bulk-boundary correspondence in ZESABS. If we consider a semi-infinite superconductor with ZESABS, the induced odd-frequency pair amplitude can be expressed by a c-number defined in bulk, which we call spectral bulk-boundary correspondence. The odd-frequency pair amplitude is classified into singular part and regular one, the former part is proportional to $\sim 1/z$ (z is a complex frequency) reflecting the presence of ZESABS, and the latter one is proportional to $\sim z$ . The coefficient of the latter one diverges at the topological phase transition point. Analyzing the spectral behavior of the odd-frequency pairing is useful to understand the critical phenomena near topological transition points.

We investigate the massive Schwinger model in $d=1+1$ dimensions using bosonization and the nonperturbative functional renormalization group. In agreement with previous studies we find that the phase transition, driven by a change of the ratio $m/e$ between the mass and the charge of the fermions, belongs to the two-dimensional Ising universality class. The temperature and vacuum angle dependence of various physical quantities (chiral density, electric field, entropy density) are also determined and agree with results obtained from density matrix renormalization group studies. Screening of fractional charges and deconfinement occur only at infinite temperature. Our results exemplify the possibility to obtain virtually all physical properties of an interacting system from the functional renormalization group., 14 pages, 9 figures

We study the semiclassical limit of a class of invariant tensors for infinite-dimensional unitary representations of $\mathrm{SL}(2,\mathbb{C})$ of the principal series, corresponding to generalized Clebsch-Gordan coefficients with $n\geq3$ legs. We find critical configurations of the quantum labels with a power-law decay of the invariants. They describe 3d polygons that can be deformed into one another via a Lorentz transformation. This is defined viewing the edge vectors of the polygons are the electric part of bivectors satisfying a (frame-dependent) relation between their electric and magnetic parts known as $\gamma$-simplicity in the loop quantum gravity literature. The frame depends on the SU(2) spin labelling the basis elements of the invariants. We compute a saddle point approximation using the critical points and provide a leading-order approximation of the invariants. The power-law is universal if the SU(2) spins have their lowest value, and $n$-dependent otherwise. As a side result, we provide a compact formula for $\gamma$-simplicity in arbitrary frames. The results have applications to the current EPRL model, but also to future research aiming at going beyond the use of fixed time gauge in spin foam models., Comment: 29 pages and 3 figures. v2:minor corrections and a subsection added to match published version

In this current paper, we purpose a ferrielectric mixed (7/2;2) spins Ising model to describe the dendrimer superlattice using Monte Carlo study (MCs). The ground state phase diagrams of dendrimer ...

Within the field-theory approach, the critical behavior of disordered spin systems with frozen point impurities and additional dipole–dipole interactions is investigated. The system is described by the Heisenberg model. The computation is performed in a two-loop approximation in three-dimensional space. The Pade–Borel method is used to sum asymptotic series. It is shown that a threshold value of the dipole–dipole interaction intensity exists such that the influence of point frozen impurities becomes important once the value exceeds this threshold. For small values of the dipole–dipole interaction intensity, the dependence of critical exponents on it is obtained.

Many complex systems exhibit large fuctuations both across space and over time. These fuctuations have often been linked to the presence of some kind of critical phenomena, where it is well known that the emerging correlation functions in space and time are closely related to each other. Here we test whether the time correlation properties allow systems exhibiting a phase transition to self-tune to their critical point. We describe results in three models: the 2D Ising ferromagnetic model, the 3D Vicsek focking model and a small-world neuronal network model. We demonstrate that feedback from the autocorrelation function of the order parameter fuctuations shifts the system towards its critical point. Our results rely on universal properties of critical systems and are expected to be relevant to a variety of other settings., Instituto de Física de Líquidos y Sistemas Biológicos

Two groups of experimental data obtained in the vicinity of the critical point are discussed. Group I describes the level ht of the meniscus separating the two phases of the substance in the cell. The measurements were performed for SF6 under the condition (g = 9.8 m s–2) during an experiment conducted in a space laboratory. Group II includes data on the density of liquid and vapor measured for C6F6 along the saturation curve under terrestrial condition. In both cases, the studied two-phase sample is located in a horizontal cylindrical cell. In the second experiment, the gravitational effect was also measured along the isotherms as the dependence of the sample density on the height h measured from the bottom of the cell. An equation relating the ht level (experiment I) with such functions as the order parameter fs and the average diameter fd is derived in this work. The obtained equation describes the initial experimental data at relative temperatures τ = (T – Tc)/Tc = 2 × 10–6–0.01. An approach is considered that takes into account the influence under microgravity (g = gM ⪡ 9.8 m s–2) on the height h (experiment II). The dependences that represent fs and fd and the density of the liquid and gas phases along the saturation curve of these substances are obtained. These dependences agree satisfactorily with the results of experiments I and II in a wide temperature range and correspond to the scaling theory of critical phenomena.

We present recent results on dynamical chiral symmetry breaking in (2 + 1)-dimensional QED with N four-component fermions. The results of the 1 / N expansion in the leading and next-to-leading orders were found exactly in an arbitrary nonlocal gauge.

A solution to an Einstein--Maxwell--dilaton-type theory with $M$ Liouville potentials and $N$ gauge fields is presented, where $M$ and $N$ are arbitrary integers. This exact solution interpolates between the Lifshitz black hole and the topological dilaton black hole. The thermodynamic behaviour of the solution is found to be similar to that of the Lifshitz black hole, where a phase transition may occur for sufficiently small charge in the canonical ensemble, or sufficiently small potential in the grand canonical ensemble., 30 pages, 5 figures. Typos corrected and more details have been added

Steady adiabatic filtration of real gases is studied. Thermodynamical states of real gases are presented by Legendrian surfaces in 5-dimensional thermodynamical contact space. The relation between phase transitions and singularities of projection of the Legendrian surfaces on the plane of intensive variables is shown. The constructive method of finding solutions of the Dirichlet filtration problem together with analysis of critical phenomena is presented. Case of van der Waals gas is discussed in details.

In this paper, we have investigated the effect of magnetic field numerically as well as analytically for holographic insulator/superconductor phase transition in higher dimensional Gauss-Bonnet gravity. First we have analysed the critical phenomena with magnetic field using two different numerical methods, namely, quasinormal modes method and the shooting method. Then we have carried out our calculation analytically using the St$\ddot{u}$rm-Liouville eigenvalue method. The methods show that marginally stable modes emerge at critical values of the chemical potential and the magnetic field satisfying the relation $\Lambda^2\equiv\mu^2-B$. We observe that the value of the chemical potential and hence the value of $\Lambda$ increases with higher values of the Gauss-Bonnet parameter and dimension of spacetime for a fixed mass of the scalar field. This clearly indicates that the phase transition from insulator to superconductor becomes difficult in the presence of the magnetic field for higher values of the Gauss-Bonnet parameter and dimension of spacetime. Our analytic results are in very good agreement with our numerical results., Comment: 14 pages, 3 figures

Universality is a principle that fundamentally underlies many critical phenomena, ranging from epidemic spreading to the emergence or breakdown of global connectivity in networks. Percolation, the transition to global connectedness on gradual addition of links, may exhibit substantial gaps in the size of the largest connected network component. We uncover that the largest gap statistics is governed by extreme-value theory. This allows us to unify continuous and discontinuous percolation by virtue of universal critical scaling functions, obtained from normal and extreme-value statistics. Specifically, we show that the universal scaling function of the size of the largest gap is given by the extreme-value Gumbel distribution. This links extreme-value statistics to universality and criticality in percolation. Percolation transitions underpin a generic class of phenomena associated with the degree of connectedness in networks. A detailed numerical study now uncovers a universal scaling in the size of the largest cluster identified in such percolation models.

We use holography to develop a physical picture of the real-time evolution of the spinodal instability of a four-dimensional, strongly-coupled gauge theory with a first-order, thermal phase transition. We numerically solve Einstein's equations to follow the evolution, in which we identify four generic stages: A first, linear stage in which the instability grows exponentially; a second, non-linear stage in which peaks and/or phase domains are formed; a third stage in which these structures merge; and a fourth stage in which the system finally relaxes to a static, phase-separated configuration. On the gravity side the latter is described by a static, stable, inhomogeneous horizon. We conjecture and provide evidence that all static, non-phase separated configurations in large enough boxes are dynamically unstable. We show that all four stages are well described by the constitutive relations of second-order hydrodynamics that include all second-order gradients that are purely spatial in the local rest frame. In contrast, a M\"uller-Israel-Stewart-type formulation of hydrodynamics fails to provide a good description for two reasons. First, it misses some large, purely-spatial gradient corrections. Second, several second-order transport coefficients in this formulation, including the relaxation times $\tau_\pi$ and $\tau_\Pi$, diverge at the points where the speed of sound vanishes., Comment: 45 pages, 35 figures; published version

The stochastic structure of polycrystalline materials causes a high inhomogeneity of the kinematic and force fields in grains of materials and large fluctuations of these fields. The inhomogeneity and fluctuations are insignificant in some cases, but they become crucial in the study of various critical phenomena whose occurrence strongly depends on the type of material microstructure. Fluctuations mainly arise due to the elastic interaction of grains, which has a long-range effect. Therefore, it is necessary to account for the interaction of a large number of grains, which is difficult to do using conventional methods (direct computer modeling and others). In the present paper, inhomogeneous mesostrain fluctuations in grains of polycrystalline materials were estimated using a field-theoretical approach to a boundary-value problem of microheterogeneous material deformation. Particular attention is paid to the calculation of extreme fluctuations that are important for some critical phenomena, such as, e.g., crack initiation under gigacycle fatigue when the macrostress amplitude and the mean stresses in grains are much lower than the quantities included in any macroscopic damage or fatigue criteria. Phe maximum mesostrains in grains can exceed several times the macrostrains. Extreme fluctuations in a grain are generated in grain clusters of specific configuration. Phe applied approach makes it possible to predict patterns of such clusters. Extreme fluctuations in the bulk grains of a polycrystalline body are much higher than in the surface grains, due to which the behavior of the material surface layers and bulk volumes is different. Quantitative data are given for the case of uniaxial tension of polycrystalline zinc.

We investigate some critical phenomena of a Ising ferrimagnetic system on a square lattice with spins $Q=\pm 7/2, \pm 5/2, \pm 3/2$ , and ±1/2 in a $B$ sublattice and spins $S=\pm 5/2, \pm 3/2$ , and ±1/2 in a $A$ sublattice in presence of an $h'$ external magnetic field, such that $Q$ and $S$ are the nearest-neighbors ferrimagnetically coupled. Using Monte Carlo simulations, we calculate the finite-temperature phase diagrams of magnetization, specific heat, and magnetic susceptibility of the model. The system is defined by a Hamiltonian $(\mathcal {H})$ that contains ferromagnetic next-nearest-neighbors interactions between $S$ spins ( $J'_{2}$ ), as well as external magnetic field and anisotropy interactions at each point of lattice. For a defined range of parameters in $\mathcal {H}$ , the system exhibits discontinuities in their physical variables and spin compensation behaviors. In the planes $J'_{2}-k_{\mathrm{ B}}T'$ and $h'-k_{\mathrm{ B}}T'$ , we analyze the relationship between the critical, compensation, and discontinuous phase transition temperatures with the external magnetic field and the next-nearest-neighbors interaction between $S$ spins. We found that the existence of discontinuous phase transition depends on the strengths of $h'$ and $J'_{2}$ .

International audience; We compare the phase diagram for vanishing chemical potential of the recently advanced version of the PNJL approach with that of the standard (P)NJL approaches.

The phase transitions and the thermodynamic properties of the two-dimensional ferromagnetic Potts model with the number of spin states q = 4 on a triangular lattice are studied on the base of the Wang–Landau algorithm of the Monte Carlo method. The phase transition characters are analyzed using the method of the four-order Binder cumulants and the histogram analysis of the data. It is found that a first-order phase transition is observed in the model under study.

We search for a first-order phase transition gravitational wave signal in 45 pulsars from the NANOGrav 12.5 year dataset. We find that the data can be modeled in terms of a strong first order phase transition taking place at temperatures below the electroweak scale. However, we do not observe any strong preference for a phase-transition interpretation of the signal over the standard astrophysical interpretation in terms of supermassive black holes mergers; but we expect to gain additional discriminating power with future datasets, improving the signal to noise ratio and extending the sensitivity window to lower frequencies. An interesting open question is how well gravitational wave observatories could separate such signals., Comment: 13 pages, 4 figures. v2: updated to match published version

Identifying the relevant coarse-grained degrees of freedom in a complex physical system is a key stage in developing powerful effective theories in and out of equilibrium. The celebrated renormalization group provides a framework for this task, but its practical execution in unfamiliar systems is fraught with ad hoc choices, whereas machine learning approaches, though promising, often lack formal interpretability. Recently, the optimal coarse-graining in a statistical system was shown to exist, based on a universal, but computationally difficult information-theoretic variational principle. This limited its applicability to but the simplest systems; moreover, the relation to standard formalism of field theory was unclear. Here we present an algorithm employing state-of-art results in machine-learning-based estimation of information-theoretic quantities, overcoming these challenges. We use this advance to develop a new paradigm in identifying the most relevant field theory operators describing properties of the system, going beyond the existing approaches to real-space renormalization. We evidence its power on an interacting model, where the emergent degrees of freedom are qualitatively different from the microscopic building blocks of the theory. Our results push the boundary of formally interpretable applications of machine learning, conceptually paving the way towards automated theory building., Comment: Version accepted for publication in Physical Review Letters. See also the companion manuscript arXiv:2103.16887 "Symmetries and phase diagrams with real-space mutual estimation neural estimation"

Real-space mutual information (RSMI) was shown to be an important quantity, formally and from a numerical standpoint, in finding coarse-grained descriptions of physical systems. It very generally quantifies spatial correlations, and can give rise to constructive algorithms extracting relevant degrees of freedom. Efficient and reliable estimation or maximization of RSMI is, however, numerically challenging. A recent breakthrough in theoretical machine learning has been the introduction of variational lower bounds for mutual information, parametrized by neural networks. Here we describe in detail how these results can be combined with differentiable coarse-graining operations to develop a single unsupervised neural-network based algorithm, the RSMI-NE, efficiently extracting the relevant degrees of freedom in the form of the operators of effective field theories, directly from real-space configurations. We study the information contained in the statistical ensemble of constructed coarse-graining transformations, and its recovery from partial input data using a secondary machine learning analysis applied to this ensemble. In particular, we show how symmetries, also emergent, can be identified. We demonstrate the extraction of the phase diagram and the order parameters for equilibrium systems, and consider also an example of a non-equilibrium problem., Accepted version. Added new discussion of symmetries in the ensemble of coarse-graining rules. 27 pages, 13 figures. arXiv admin note: substantial text overlap with arXiv:2101.11633

We carry out numerical simulations of the gravitational collapse of a rotating perfect fluid with the ultrarelativistic equation of state $P=\kappa\rho$, in axisymmetry in $2+1$ spacetime dimensions with $\Lambda, Comment: 14 pages, 8 figures. Typos corrected. This version has been accepted by PRD

We find stationary thin-brane geometries that are dual to far-from-equilibrium steady states of two-dimensional holographic interfaces. The flow of heat at the boundary agrees with the result of CFT and the known energy-transport coefficients of the thin-brane model. We argue that by entangling outgoing excitations the interface produces coarse-grained entropy at a maximal rate, and point out similarities and differences with double-sided black funnels. The non-compact, non-Killing and far from-equilibrium event horizon of our solutions coincides with the local (apparent) horizon on the colder side, but lies behind it on the hotter side of the interface. We also show that the thermal conductivity of a pair of interfaces jumps at the Hawking-Page phase transition from a regime described by classical scatterers to a quantum regime in which heat flows unobstructed., 40 pages, 8 figures Added few discussion paragraphs

Using a description of the Levin-Wen model excitations in terms of Wilson lines, we compute the degeneracy of the energy levels for any input anyon theory and for any trivalent graph embedded on any (orientable) compact surface. This result allows one to obtain the finite-size and finite-temperature partition function and to show that there are no thermal phase transitions., Comment: 7 pages, 2 figures, published version

Drawing on an analogy to critical phenomena, it was shown that the Nikuradse turbulent friction factor ($f_t$) measurements in pipes of radius $R$ and wall roughness $r$ can be collapsed onto a one-dimensional curve expressed as a conveyance law $f_t Re^{1/4}=g_o(\chi)$, where $Re$ is a bulk Reynolds number, $\chi =Re^{3/4}\left({r}/{R}\right)$. The implicit function $g_o(.)$ was conjectured based on matching two asymptotic limits of $f_t$. However, the connection between $g_o(.)$ and the phenomenon it proclaims to represent - turbulent eddies - remains lacking. Using models for the wall-normal velocity spectrum and return-to-isotropy for pressure-strain effects to close a co-spectral density budget, a derivation of $g_o(.)$ is offered. The proposed method explicitly derives the solution of the conveyance law and provides a physical interpretation of $\chi$ as a dimensionless length scale reflecting the competition between viscous sublayer thickness and characteristic height of roughness elements. The application of the proposed method to other published measurements spanning roughness and Reynolds numbers beyond the original Nikuradse range is further discussed.

Stochastic quantization provides an alternate approach to the computation of quantum observables, by stochastically sampling phase space in a path integral. Furthermore, the stochastic variational method can provide analytical control over the strong coupling regime of a quantum field theory -- provided one has a decent qualitative guess at the form of certain observables at strong coupling. In the context of the holographic duality, the strong coupling regime of a Yang-Mills theory can capture gravitational dynamics. This can provide enough insight to guide a stochastic variational ansatz. We demonstrate this in the bosonic Banks-Fischler-Shenker-Susskind Matrix theory. We compute a two-point function at all values of coupling using the variational method showing agreement with lattice numerical computations and capturing the confinement-deconfinement phase transition at strong coupling. This opens up a new realm of possibilities for exploring the holographic duality and emergent geometry., 24 pages, 5 figures; v2: added citations

We study how chaos, introduced by a weak perturbation, affects the reliability of the output of analog quantum simulation. As a toy model, we consider the Lipkin-Meshkov-Glick (LMG) model. Inspired by the semiclassical behavior of the order parameter in the thermodynamic limit, we propose a protocol to measure the quantum phase transition in the ground state and the dynamical quantum phase transition associated with quench dynamics. We show that the presence of a small time-dependent perturbation can render the dynamics of the system chaotic. We then show that the estimates of the critical points of these quantum phase transitions, obtained from the quantum simulation of its dynamics, are robust to the presence of this chaotic perturbation, while other aspects of the system, such as the mean magnetization are fragile, and therefore cannot be reliably extracted from this simulator. This can be understood in terms of the simulated quantities that depend on the global structure of phase space vs. those that depend on local trajectories., Comment: 13 pages, 7 figures

We study the Chiral Separation Effect (CSE) in finite-density SU(2) lattice gauge theory with dynamical quarks. We find that the CSE is well described by the free quark result in the high-temperature quark-gluon plasma phase. As one enters the confinement regime with broken chiral symmetry at chemical potential smaller than half of the pion mass, the CSE response is gradually suppressed towards low temperatures in comparison to the free quark result. This suppression can be approximately described by assuming that the CSE current is proportional to the charge density, rather than the chemical potential, as suggested in the literature (ArXiv:1712.01256, Phys.Rev.D97(2018)085020). We also provide an upper bound on the contribution of disconnected fermionic diagrams to the CSE, which is consistent with zero within our statistical errors and small compared to that of the connected diagrams. Our results are obtained mainly in the QCD-like regime of SU(2) gauge theory at low densities, and hence should be at least qualitatively applicable to QCD as well., v2: published version, 10 pages RevTeX, 6 figures

We report on a combined experimental and theoretical study of the low-entropy Mott transition for interacting bosons trapped in a three-dimensional (3D) cubic lattice -- namely, the interaction-induced superfluid-to-normal phase transition in the vicinity of the zero-temperature Mott transition. Our analysis relies on the measurement of the 3D momentum distribution, which allows us to extract the momentum-space density $\rho({\bf k}={\bf 0})$ at the center of the Brillouin zone. Upon varying the ratio between the interaction $U$ and the tunnelling energy $J$ across the superfluid transition, we observe that $\rho({\bf k}={\bf 0})$ exhibits a sharp transition at a value of $U/J$ consistent with the bulk prediction from quantum Monte Carlo. In addition, the variation of $\rho({\bf k}={\bf 0})$ with $U/J$ exhibits a critical behavior consistent with the expected 3D XY universality class. Our results show that the tomographic reconstruction of the momentum distribution of ultracold bosons can reveal traits of the critical behavior of the superfluid transition even in an inhomogeneous trapped system., Comment: 5 pages, 4 figures

We present a model compound with a spin-1/2 spatially anisotropic frustrated square lattice, in which three antiferromagnetic interactions and one ferromagnetic interaction are competing. We observe an unconventional gradual increase in the low-temperature magnetization curve reminiscent of the quantum critical behavior between gapped and gapless phases. In addition, the specific heat and electron spin resonance signals indicate one-dimensional characteristics. These results demonstrate quantum critical behavior associated with one dimensionalization caused by frustrated interactions in the spin-1/2 spatially anisotropic square lattice., Comment: 6 pages, 4 figures

We study the operator product expansion of stress tensors (TT OPE) in d>2 conformal field theories whose bulk dual is Einstein gravity. Directly from the TT OPE, we obtain, in a certain null-like limit, an algebraic structure consistent with the Jacobi identity: [Lm,Ln]=(m−n)Lm+n+Cm(m2−1)δm+n,0. The dimensionless constant C is proportional to the central charge CT. Transverse integrals in the definition of Lm play a crucial role. We comment on the corresponding limiting procedure and point out a curiosity related to the central term. A connection between the d>2 near-lightcone stress-tensor conformal block and the d=2 W algebra is observed. This note is motivated by the search for a field-theoretic derivation of d>2 correlators in strong coupling critical phenomena.

We present a novel framework to solve simultaneously the electroweak hierarchy problem and the strong-CP problem. A small but finite Higgs vacuum expectation value and a small $\theta$-angle are selected after the QCD phase transition, without relying on the Peccei-Quinn mechanism or other traditional solutions. We predict a distinctive pattern of correlated signals at hadronic EDM, fuzzy dark matter and axion experiments. We present a novel framework to solve simultaneously the electroweak-hierarchy problem and the strong-CP problem. A small but finite Higgs vacuum expectation value and a small θ angle are selected after the QCD phase transition, without relying on the Peccei-Quinn mechanism or other traditional solutions. We predict a distinctive pattern of correlated signals at hadronic EDM, fuzzy dark matter, and axion experiments.

International audience; When supersymmetry is spontaneously broken at the tree level, the spectrum of the heterotic string compactified on orbifolds of tori contains an infinite number of potentially tachyonic modes. We show that this implies instabilities of Minkowski space–time, when the scale of supersymmetry breaking is of the order of the string scale. We derive the phase space structure of vacua in the case where the tachyonic spectrum contains a mode with trivial momenta and winding numbers along the internal directions not involved in the supersymmetry breaking.

The spectrum of bound states of special strongly coupled confining field theories might include a parametrically light dilaton, associated with the formation of enhanced condensates that break (approximate) scale invariance spontaneously. It has been suggested in the literature that such a state may arise in connection with the theory being close to the unitarity bound in holographic models. We extend these ideas to cases where the background geometry is non-AdS, and the gravity description of the dual confining field theory has a top-down origin in supergravity. We exemplify this programme by studying the circle compactification of Romans six-dimensional half-maximal supergravity. We uncover a rich space of solutions, many of which were previously unknown in the literature. We compute the bosonic spectrum of excitations, and identify a tachyonic instability in a region of parameter space for a class of regular background solutions. A tachyon only exists along an energetically disfavoured (unphysical) branch of solutions of the gravity theory; we find evidence of a first-order phase transition that separates this region of parameter space from the physical one. Along the physical branch of regular solutions, one of the lightest scalar particles is approximately a dilaton, and it is associated with a condensate in the underlying theory. Yet, because of the location of the phase transition, its mass is not parametrically small, and it is, coincidentally, the next-to-lightest scalar bound state, rather than the lightest one., Comment: Version accepted for publication

Nonequilibrium critical phenomena generally exist in many dynamic systems, like chemical reactions and some driven-dissipative reactive particle systems. Here, by using computer simulation and theoretical analysis, we demonstrate the crucial role of the activation barrier on the criticality of dynamic phase transitions in a minimal reactive hard-sphere model. We find that at zero thermal noise, with increasing the activation barrier, the type of transition changes from a continuous conserved directed percolation into a discontinuous dynamic transition by crossing a tricritical point. A mean-field theory combined with field simulation is proposed to explain this phenomenon. The possibility of Ising-type criticality in the nonequilibrium system at finite thermal noise is also discussed. Agency for Science, Technology and Research (A*STAR) Ministry of Education (MOE) Nanyang Technological University Published version This work has been supported in part by the Singapore Ministry of Education through the Academic Research Fund MOE2019-T2-2-010 and RG104/17 (S), by Nanyang Technological University Start-Up Grant (NTUSUG: M4081781.120), by the Advanced Manufacturing and Engineering Young Individual Research Grant (A1784C0018) and by the Science and Engineering Research Council of Agency for Science, Technology and Research Singapore, by the National Natural Science Foundation of China under Grant No. 11905001.

Based on expansions with only two coefficients and known critical points, we consider a minimal model of critical phenomena. The method of analysis is both based on and inspired with the symmetry properties of functional self-similarity relation between the consecutive functional approximations. Factor approximants are applied together with various natural optimization conditions of non-perturbative nature. The role of control parameter is played by the critical index by itself. The minimal derivative condition imposed on critical amplitude appears to bring the most reasonable, uniquely defined results. The minimal difference condition also imposed on amplitudes produces upper and lower bound on the critical index. While one of the bounds is close to the result from the minimal difference condition, the second bound is determined by the non-optimized factor approximant. One would expect that for the minimal derivative condition to work well, the bounds determined by the minimal difference condition should be not too wide. In this sense the technique of optimization presented above is self-consistent, since it automatically supplies the solution and the bounds. In the case of effective viscosity of passive suspensions the bounds could be found that are too wide to make any sense from either of the solutions. Other optimization conditions imposed on the factor approximants, lead to better estimates for the critical index for the effective viscosity. The optimization is based on equating two explicit expressions following from two different definitions of the critical index, while optimization parameter is introduced as the trial third-order coefficient in the expansion.

Spontaneous decay of a single photon is a notoriously inefficient process in nature irrespective of the frequency range. We report that a quantum phase-slip fluctuation in high-impedance superconducting waveguides can split a single incident microwave photon into a large number of lower-energy photons with a near unit probability. The underlying inelastic photon-photon interaction has no analogs in non-linear optics. Instead, the measured decay rates are explained without adjustable parameters in the framework of a new model of a quantum impurity in a Luttinger liquid. Our result connects circuit quantum electrodynamics to critical phenomena in two-dimensional boundary quantum field theories, important in the physics of strongly-correlated systems. The photon lifetime data represents a rare example of verified and useful quantum many-body simulation., minor revision for clarity, supplementary material is available at www.superconducting-circuits.com

The BPS bound states of D4-D2-D0 branes on the noncompact divisors of Calabi-Yau threefolds and the instantons in the dual quiver gauge theories are previously studied using two-dimensional crystal melting model and dimer model, [T. Nishinaka et al., J. High Energy Phys. 5 (2014) 139]. Using the tropical geometry associated with the toric quiver, we study the asymptotic of the quiver gauge theory to compute some of their thermodynamic observables and extract the phase structure. We obtain that the thermodynamic observables such as free energy, entropy, and growth rate are explicitly derived from the limit shape of the crystal model, the boundary of the amoeba and its Harnack curve characterization. Furthermore, we observe that there is a Hagedorn phase transition in the instanton sector inferred from the Gumbel distribution of the fluctuations in the crystal model. We present explicit computations of the results in concrete examples of C3, conifold, local P1×P1 and local P2 quivers.

Percolation models shed a light on network integrity and functionality and have numerous applications in network theory. This paper studies a targeted percolation ($\ensuremath{\alpha}$ model) with incomplete knowledge where the highest degree node in a randomly selected set of $n$ nodes is removed at each step, and the model features a tunable probability that the removed node is instead a random one. A ``mirror image'' process ($\ensuremath{\beta}$ model) in which the target is the lowest degree node is also investigated. We analytically calculate the giant component size, the critical occupation probability, and the scaling law for the percolation threshold with respect to the knowledge level $n$ under both models. We also derive self-consistency equations to analyze the $k$-core organization including the size of the $k$ core and its corona in the context of attacks under tunable limited knowledge. These percolation models are characterized by some interesting critical phenomena and reveal profound quantitative structure discrepancies between Erd\ifmmode \mbox{\H{o}}\else \H{o}\fi{}s-R\'enyi networks and power-law networks.