The non-equilibrium dynamics of an isolated quantum system after a sudden quench to a dynamical critical point is expected to be characterized by scaling and universal exponents due to the absence of time scales. We explore these features for a quench of the parameters of a Hamiltonian with $O(N)$ symmetry, starting from a ground state in the disordered phase. In the limit of infinite $N$, the exponents and scaling forms of the relevant two-time correlation functions can be calculated exactly. Our analytical predictions are confirmed by the numerical solution of the corresponding equations. Moreover, we find that the same scaling functions, yet with different exponents, also describe the coarsening dynamics for quenches below the dynamical critical point.
Using Monte Carlo simulations, we have studied the relaxation of energy of the three-dimensional Ising spin-glass model in aging process. Our finite-size-scaling analysis on the isothermal energy decay after the quench suggests strongly that the energy relaxes by coarsening of domain walls in agreement with the droplet theory. We have also evaluated relaxation times required for spin configurations in small systems, which are regarded as isolated droplets, to flip globally. The results support the fundamental assumption of the droplet theory that coarsening of domain walls, in case of spin gla…
We investigate the early coarsening dynamics of an atomic Bose gas quenched into a superfluid phase. Using a two-step quench protocol, we effectively control the cooling rates, $r_1$ and $r_2$, during and after passing through the critical region, respectively, and measure the number of quantum vortices spontaneously created in the system. The latter cooling rate $r_2$ regulates the temperature during the condensate growth, consequently controlling the early coarsening dynamics in the defect formation. We find that the defect number shows a scaling behavior with $r_2$ regardless of the initial…
Using extensive Monte Carlo simulations we study aging properties of two disordered systems quenched below their critical point, namely the two-dimensional random-bond Ising model and the three-dimensional Edwards-Anderson Ising spin glass with a bimodal distribution of the coupling constants. We study the two-times autocorrelation and space-time correlation functions and show that in both systems a simple aging scenario prevails in terms of the scaling variable $L(t)/L(s)$, where $L$ is the time-dependent correlation length, whereas $s$ is the waiting time and $t$ is the observation time. The…
We comprehensively study non-equilibrium relaxation and aging processes in the two-dimensional random-site Ising model through numerical simulations. We discuss the dynamical correlation length as well as scaling functions of various two-times quantities as a function of temperature and of the degree of dilution. For already modest values of the dynamical correlation length $L$ deviations from a simple algebraic growth, $L(t) \sim t^{1/z}$, are observed. When taking this non-algebraic growth properly into account, a simple aging behavior of the autocorrelation function is found. This is in sta…
The non-equilibrium dynamics of a system that is located in the vicinity of a quantum critical point is affected by the critical slowing down of order-parameter correlations with the potential for novel out-of-equilibrium universality. After a quantum quench, i.e. a sudden change of a parameter in the Hamiltonian such a system is expected to almost instantly fall out of equilibrium and undergo aging dynamics, i.e. dynamics that depends on the time passed since the quench. Investigating the quantum dynamics of a $N$-component $φ^{4}$-model coupled to an external bath, we determine this universa…
We present results for the nonequilibrium dynamics of collapse for a model flexible homopolymer on simple cubic lattices with fixed and fluctuating bonds between the monomers. Results from our Monte Carlo simulations show that, phenomenologically, the sequence of events observed during the collapse are independent of the bond criterion. While the growth of the clusters (of monomers) at different temperatures exhibits a nonuniversal power-law behavior when the bonds are fixed, the introduction of fluctuations in the bonds by considering the existence of diagonal bonds produces a temperature ind…
We overview the general scaling behavior of the effective temperature in the que nches of simple non disordered systems, like ferromagnets, to and below $T_C$. Emphasis is on the behavior as d imensionality is varied. Consequences on the shape of the asymptotic parametric representation are derived. In particu lar, this is always trivial in the critical quenches with $T_C>0$. We clarify that the quench to $T_C=0$ at the lower critical dimensionality $d_L$, cannot be regarded as a critical quench. Implications for the behavior of the exponent $a$ of the aging response function in the quenches b…
Following quenches from random initial configurations to zero temperature, we study aging during evolution of the ferromagnetic (nonconserved) Ising model towards equilibrium, via Monte Carlo simulations of very large systems, in space dimensions $d=2$ and $3$. Results for the two-time autocorrelations, obtained by using different acceptance probabilities for the spin-flip trial moves, are in agreement with each other. We demonstrate the scaling of this quantity with respect to $\ell/\ell_w$, where $\ell$ and $\ell_w$ are the average domain sizes at $t$ and $t_w$ $(\leqslant t)$, the observati…
The complex Ginzburg-Landau equation with additive noise is a stochastic partial differential equation that describes a remarkably wide range of physical systems which include coupled non-linear oscillators subject to external noise near a Hopf bifurcation instability and spontaneous structure formation in non-equilibrium systems, e.g., in cyclically competing populations or oscillatory chemical reactions. We employ a finite-difference method to numerically solve the noisy complex Ginzburg-Landau equation on a two-dimensional domain with the goal to investigate its non-equilibrium dynamics whe…
The quantum O(N) model in the infinite $N$ limit is a paradigm for symmetry-breaking. Qualitatively, its phase diagram is an excellent guide to the equilibrium physics for more realistic values of $N$ in varying spatial dimensions ($d>1$). Here we investigate the physics of this model out of equilibrium, specifically its response to global quenches starting in the disordered phase. If the model were to exhibit equilibration, the late time state could be inferred from the finite temperature phase diagram. In the infinite $N$ limit, we show that not only does the model not lead to equilibration …
Quantum quenches to or near criticality give rise to the phenomenon of \textit{aging}, manifested by glassy-like dynamics at short times and far from equilibrium. The recent surge of interest in the dynamics of quantum many-body systems has rejuvenated interest in this phenomenon. Motivated by the ubiquitous long-range interactions in emerging experimental platforms, it is vital to study quantum aging in such settings. In this work, we investigate the dynamical universality and aging in the $d$-dimensional $O(N)$ model with the long-range coupling $1/x^{d+σ}$ and in the mean-field limit $N\to\…
Aging, the dependence of the dynamics of a physical process on the time $t_a$ since its original preparation, is observed in systems ranging from the motion of charge carriers in amorphous semiconductors over the blinking dynamics of quantum dots to the tracer dispersion in living biological cells. Here we study the effects of aging on one of the most fundamental properties of a stochastic process, the first passage dynamics. We find that for an aging continuous time random walk process the scaling exponent of the density of first passage times changes twice as the aging progresses and reveals…
Via Monte Carlo simulations we study nonequilibrium dynamics in the nearest-neighbor Ising model, following quenches to points inside the ordered region of the phase diagram. With the broad objective of quantifying the nonequilibrium universality classes corresponding to spatially correlated and uncorrelated initial configurations, in this paper we present results for the decay of the order-parameter autocorrelation function for quenches from the critical point. This autocorrelation is an important probe for the aging dynamics in far-from-equilibrium systems and typically exhibits power-law sc…
We study the geometric properties of polymixtures after a sudden quench in temperature. We mimic these systems with the $q$-states Potts model on a square lattice with and without weak quenched disorder, and their evolution with Monte Carlo simulations with non-conserved order parameter. We analyze the distribution of hull enclosed areas for different initial conditions and compare our results with recent exact and numerical findings for $q=2$ (Ising) case. Our results demonstrate the memory of the presence or absence of long-range correlations in the initial state during the coarsening regime…
We study the fate of the 2d kinetic q-state Potts model after a sudden quench to zero temperature. Both ground states and complicated static states are reached with non-zero probabilities. These outcomes resemble those found in the quench of the 2d Ising model; however, the variety of static states in the q-state Potts model (with q>=3) is much richer than in the Ising model, where static states are either ground or stripe states. Another possibility is that the system gets trapped on a set of equal-energy blinker states where a subset of spins can flip ad infinitum; these states are similar t…
Using numerical simulations we investigate the space-time properties of a system in which spirals emerge within coarsening domains, thus giving rise to non-trivial internal dynamics. Initially proposed in the context of population dynamics, the studied six-species model exhibits growing domains composed of three species in a rock-paper-scissors relationship. Through the investigation of different quantities, such as space-time correlations and the derived characteristic length, autocorrelation, density of empty sites, and interface width, we demonstrate that the non-trivial dynamics inside the…
We consider the $d$-dimensional transverse-field Ising model with power-law interactions $J/r^{d+σ}$ in the presence of a noisy longitudinal field with zero average. We study the longitudinal-magnetization dynamics of an initial paramagnetic state after a sudden switch-on of both the interactions and the noisy field. While the system eventually relaxes to an infinite-temperature state with vanishing magnetization correlations, we find that two-time correlation functions show aging at intermediate times. Moreover, for times shorter than the inverse noise strength $κ$ and distances longer than $…
We study numerically the aging dynamics of the two-dimensional p-state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior characteristic of non-disordered coarsening systems. For quenches to the ferromagnetic phase, the value of the dynamical exponents, suggests that the model belongs to the Ising-type universality class. Specifically, for the integrated response function $χ(t,s)\simeq s^{-a_χ}f(t/s)$, we find $a_χ$ consistent with the value $a_χ=0.28$ found in the two-dimensio…
Mixtures of glass-forming fluids sometimes exhibit glass-glass phase separation at low temperatures. Here, we use a molecular dynamics simulation to study one of the simplest examples of the glass-glass phase separation. We consider a mixture composed of type A and B particles, in which the A-A and B-B interactions are the identical Lennard-Jones interactions and the A-B interaction is repulsive only. To avoid crystallization, we also introduce the polydispersity in the particle sizes for each component. We study the phase separation kinetics of this model at a 50:50 concentration at various t…
Several mean-field computations have revealed the existence of an out of equilibrium dynamical transition induced by quantum quenching an isolated system starting from its symmetry broken phase. In this work we focus on the quantum phi^4 N-component field theory. By taking into account dynamical fluctuations at the Hartree-Fock level, corresponding to the leading order of the 1/N expansion, we derive the critical properties of the dynamical transition beyond mean-field theory (including at finite temperature). We find diverging time and length-scales, dynamic scaling and aging. Finally, we unv…
Using molecular dynamics simulations we study the out of equilibrium dynamic correlations in a model glass-forming liquid. The system is quenched from a high temperature to a temperature below its glass transition temperature and the decay of the two-time intermediate scattering function C(t_w,t+t_w) is monitored for several values of the waiting time t_w after the quench. We find that C(t_w,t+t_w) shows a strong dependence on the waiting time, i.e. aging, depends on the temperature before the quench and, similar to the case of spin glasses, can be scaled onto a master curve.
We investigate numerically the dynamics of three different spin models in the aging regime. Each of these models is meant to be representative of a distinct class of aging behavior: coarsening systems, discontinuous spin glasses, and continuous spin glasses. In order to study dynamic heterogeneities induced by quenched disorder, we consider single-spin observables for a given disorder realization. In some simple cases we are able to provide analytical predictions for single-spin response and correlation functions. The results strongly depend upon the model considered. It turns out that, by com…
Pinning particles at random in supercooled liquids is a promising route to make substantial progress on the glass transition problem. Here we develop a mean-field theory by studying the equilibrium and non-equilibrium dynamics of the spherical p-spin model in presence of a fraction c of pinned spins. Our study shows the existence of two dynamic critical lines: one corresponding to usual Mode Coupling transitions and the other one to dynamic spinodal transitions. Quenches in the portion of the c - T phase diagram delimited by those two lines leads to aging. By extending our results to finite di…
In this article, we present a Monte Carlo study of phase transition and coarsening dynamics in the non-conserved two-dimensional random-bond $q$-state clock model (RBCM) deriving from a pure clock model [Phys. Rev. E 98, 032109 (2018)]. Akin to the pure clock model, RBCM also passes through two different phases when quenched from a disordered initial configuration representing at infinite temperature. Our investigation of the equilibrium phase transition affirms that both upper ($T_c^1$) and lower ($T_c^2$) phase transition temperatures decrease with bond randomness strength $ε$. Effect of $ε$…
The orientation fluctuations of the director of a liquid crystal(LC) are measured after a quench near the Fréedericksz transition, which is a second order transition driven by an electric field. We report experimental evidence that, because of the critical slowing down, the LC presents, after the quench, several properties of an aging system, such as power law scaling versus time of correlation and response functions. During this slow relaxation, a well defined effective temperature, much larger than the heat bath temperature, can be measured using the fluctuation dissipation relation.
The vortex velocity distribution function for a 2-dimensional coarsening non-conserved O(2) time-dependent Ginzburg-Landau model is determined numerically and compared to theoretical predictions. In agreement with these predictions the distribution function scales with the average vortex speed which is inversely proportional to t^x, where t is the time after the quench and x is near to 1/2. We find the entire curve, including a large speed algebraic tail, in good agreement with the theory.
Recently, different numerical studies of coarsening in disordered systems have shown the existence of a crossover from an initial, transient, power-law domain growth to a slower, presumably logarithmic, growth. However, due to the very slow dynamics and the long lasting transient regime, one is usually not able to fully enter the asymptotic regime when investigating the relaxation of these systems toward equilibrium. We here study two simple driven systems, the one-dimensional $ABC$ model and a related domain model with simplified dynamics, that are known to exhibit anomalous slow relaxation w…
Aging following a zero-temperature quench in the $d=3$ Ising model
Institut für Theoretische Physik, Universität Leipzig（莱比锡大学理论物理研究所）；Centre for Fluid and Complex Systems, Coventry University（考文垂大学流体与复杂系统中心）；NEC Laboratories Europe GmbH（NEC欧洲实验室有限公司）
We study the dynamics of the critical two-dimensional fully-frustrated Ising model by means of Monte Carlo simulations. The dynamical exponent is estimated at equilibrium and is shown to be compatible with the value $z_c=2$. In a second step, the system is prepared in the paramagnetic phase and then quenched at its critical temperature $T_c=0$. Numerical evidences for the existence of logarithmic corrections in the aging regime are presented. These corrections may be related to the topological defects observed in other fully-frustrated models. The autocorrelation exponent is estimated to be $λ…
A simple, non-disordered spin model has been studied in an effort to understand the origin of the precipitous slowing down of dynamics observed in supercooled liquids approaching the glass transition. A combination of Monte Carlo simulations and exact calculations indicates that this model exhibits an entropy vanishing transition accompanied by a rapid divergence of time scales. Measurements of various correlation functions show that the system displays a hierarchy of time scales associated with different degrees of freedom. Extended structures, arising from the frustration in the system, are …
We consider a simple model of a structural glass, represented by a lattice gas with kinetic constraints in contact with a particle reservoir. Quench below the glass transition is represented by the jump of the chemical potential above a threshold. After a quench, the density approaches the critical density-where the diffusion coefficient of the particles vanishes-following a power law in time. In this regime, the two-time self-correlation functions exhibit aging. The behavior of the model can be understood in terms of simple mean-field arguments.
In the conceptual framework of phase ordering after temperature quenches below transition, we consider the underdamped Bales-Gooding-type 'momentum conserving' dynamics of a 2D martensitic structural transition from a square-to-rectangle unit cell. The one-component or $N_{\rm OP} =1$ order parameter is one of the physical strains, and the Landau free energy has a triple well, describing a first-order transition. We numerically study the evolution of the strain-strain correlation, and find that it exhibits dynamical scaling, with a coarsening length $L(t) \sim t^α$. We find at intermediate and…
The deviations from full or pure aging behavior, i.e. perfect $t/t_w$ scaling of the correlation and response functions of aging glassy systems, are not well understood theoretically. Recent experiments of Rodriguez et al. (Phys. Rev. Lett. 91, 037203 (2003)) have shown that full aging applies to the thermoremanent magnetization in the limit of infinite cooling rate during the initial quench. In numerical models, instantaneous thermal quenches can be--and usually are--applied. This has motivated the present numerical investigations of the aging behavior of Edwards-Anderson Ising spin glass mod…
We discuss the relaxation dynamics of a simple structural glass which has been quenched below its glass transition temperature. We demonstrate that time correlation functions show strong aging effects and investigate in what way the fluctuation dissipation theorem is violated.
The domain morphology of weakly disordered ferromagnets, quenched from the high-temperature phase to the low-temperature phase, is studied using numerical simulations. We find that the geometrical properties of the coarsening domain structure, e.g., the distributions of hull enclosed areas and domain perimeter lengths, are described by a scaling phenomenology in which the growing domain scale R(t) is the only relevant parameter. Furthermore, the scaling functions have forms identical to those of the corresponding pure system, extending the 'super-universality' property previously noted for the…
We study numerically the two-dimensional Ising model with non-conserved dynamics quenched from an initial equilibrium state at the temperature $T_i\ge T_c$ to a final temperature $T_f$ below the critical one. By considering processes initiating both from a disordered state at infinite temperature $T_i=\infty$ and from the critical configurations at $T_i=T_c$ and spanning the range of final temperatures $T_f\in [0,T_c[$ we elucidate the role played by $T_i$ and $T_f$ on the aging properties and, in particular, on the behavior of the autocorrelation $C$ and of the integrated response function $χ…
The coarsening exponents describing the growth of long-range order in systems quenched from a disordered to an ordered phase are discussed in terms of the decay rate, omega(k), for the relaxation of a distortion of wavevector k applied to a topological defect. For systems described by order parameters with Z(2) (`Ising'), and O(2) (`XY') symmetry, the appropriate defects are domain walls and vortex lines respectively. From omega(k) ~ k^z, we infer L(t) ~ t^(1/z) for the coarsening scale, with the assumption that defect relaxation provides the dominant coarsening mechanism. The O(2) case requir…
Following quenches of initial configurations having long range spatial correlations, prepared at the demixing critical point, to points inside the miscibility gap, we study aging phenomena in solid binary mixtures. Results on the decay of the two-time order-parameter autocorrelation functions, obtained from Monte Carlo simulations of the two-dimensional Ising model, with Kawasaki exchange kinetics, are analyzed via state-of-the art methods. The outcome is compared with that obtained for the ordering in uniaxial ferromagnets. For the latter, we have performed Monte Carlo simulations of the same…
We construct the equations for the growth kinetics of an aging structural glass within mode-coupling theory through a non-stationary variant of the 3-density correlator defined in Phys. Rev. Lett. {\bf 97}, 195701 (2006). We solve a schematic form of the resulting equations to obtain the coarsening of the dynamic heterogeneity, characterized via the 3-point correlator $χ_3(t,t_w)$, as a function of waiting time $t_w$. For a quench into the glass, we find that $χ_3$ attains a peak value $\sim t_w^{0.5}$ at $t -t_w \sim t_w^{0.8}$, providing a theoretical basis for the numerical observations of …
Using molecular dynamics computer simulations we investigate the out-of-equilibrium dynamics of a Lennard-Jones system after a quench from a high temperature to one below the glass transition temperature. By studying the radial distribution function we give evidence that during the aging the system is very close to the critical surface of mode-coupling theory. Furthermore we show that two-time correlation functions show a strong dependence on the waiting time since the quench and that their shape is very different from the one in equilibrium. By investigating the temperature and time dependenc…
Analogies between evolutionary dynamics and statistical mechanics, such as Fisher's second-law-like "fundamental theorem of natural selection" and Wright's "fitness landscapes", have had a deep and fruitful influence on the development of evolutionary theory. Here I discuss a new conceptual link between evolution and statistical physics. I argue that natural selection can be viewed as a coarsening phenomenon, similar to the growth of domain size in quenched magnets or to Ostwald ripening in alloys and emulsions. In particular, I show that the most remarkable features of coarsening---scaling an…
We investigate the aging dynamics of amorphous SiO2 via molecular dynamics simulations of a quench from a high temperature T_i to a lower temperature T_f. We obtain a microscopic picture of aging dynamics by analyzing single particle trajectories, identifying jump events when a particle escapes the cage formed by its neighbors, and by determining how these jumps depend on the waiting time t_w, the time elapsed since the temperature quench to T_f. We find that the only t_w-dependent microscopic quantity is the number of jumping particles per unit time, which decreases with age. Similar to previ…
A long-lived prethermal state may emerge upon a sudden quench of a quantum system. In this paper, we study a quantum quench of an initial {\it critical} state, and show that the resulting prethermal state exhibits a genuinely quantum and dynamical universal behavior. Specifically, we consider a scenario where the "speed of light" characterizing the propagation of local perturbations is suddenly quenched at criticality. We also find that the system approaches the prethermal state in a universal way described by a new exponent that characterizes a kind of quantum aging.
We analyse the out of equilibrium behavior of an Ising spin chain with an asymmetric kinetic constraint after a quench to a low temperature T. In the limit T\to 0, we provide an exact solution of the resulting coarsening process. The equilibration time exhibits a `glassy' divergence \teq=\exp(const/T^2) (popular as an alternative to the Vogel-Fulcher law), while the average domain length grows with a temperature dependent exponent, \dbar ~ t^{T\ln 2}. We show that the equilibration time \teq also sets the timescale for the linear response of the system at low temperatures.
The Chapter is devoted to reviewing the main features of aging in non disordered systems relaxing via domain growth, after an istantaneous temperature quench. Using the autocorrelation and autoresponse functions to gauge the deviation from equilibrium, an hierarchy of processes is obtained by changing the temperature of the quench and the space dimensionality. The special role of the lower critical dimensionality is highlighted. Basic properties like the separation of the time scales and the splitting of degrees of freedom into fast and slow variables are treated in detail, both in general ter…
Domain growth during the kinetics of phase separation is studied following vapor-liquid transition in a single component Lennard-Jones fluid. Results are analyzed after appropriately mapping the continuum snapshots obtained from extensive molecular dynamics simulations to a simple cubic lattice. For near critical quench interconnected domain morphology is observed. A brief period of slow diffusive growth is followed by a linear viscous hydrodynamic growth that lasts for an extended period of time. This result is in contradiction with earlier inclusive reports of late time growth exponent 1/2 t…
Recent emerging interest in experiments of single-polymer dynamics urge computational physicists to revive their understandings, particularly in the nonequilibrium context. Here we briefly discuss the currently evolving approaches of investigating the evolution dynamics of homopolymer collapse in computer simulations. Primary focus of these approaches is to understand various dynamic scaling laws related to coarsening and aging during the collapse in space dimension $d=3$, using tools popular in nonequilibrium coarsening dynamics of particle or spin systems. In addition to providing an overvie…
We study dynamic fluctuations in non-disordered finite dimensional ferromagnetic systems quenched to the critical point and the low-temperature phase. We investigate the fluctuations of two two-time quantities, called $χ$ and $C$, the averages of which %$<χ>$, $<C>$ yield the self linear response and correlation function. We introduce a restricted average of the $χ$'s, summing over all configurations with a given value of $C$. We find that the restricted average $<χ>_C$ obeys a scaling form, and that the slope of the scaling function approaches the universal value $X_\infty $ of the limiting e…
We present comparative results from simulations of a lattice and an off-lattice model of a homopolymer, in the context of kinetics of the collapse transition. Scaling laws related to the collapse time, cluster coarsening and aging behavior are compared. Although in both models the cluster growth is independent of temperature, the related exponents turn out to be different. Conversely, the aging and associated scaling properties are found to be universal, with the nonequilibrium autocorrelation exponent obeying a recently derived bound.
We study the evolution of spin clusters on two dimensional slices of the $3d$ Ising model in contact with a heat bath after a sudden quench to a subcritical temperature. We analyze the evolution of some simple initial configurations, such as a sphere and a torus, of one phase embedded into the other, to confirm that their area disappears linearly in time and to establish the temperature dependence of the prefactor in each case. Two generic kinds of initial states are later used: equilibrium configurations either at infinite temperature or at the paramagnetic-ferromagnetic phase transition. We …
The non-equilibrium self-consistent generalized Langevin equation theory of irreversible processes in liquids is extended to describe the positional and orientational thermal fluctuations of the instantaneous local concentration profile $n(\mathbf{r},Ω,t)$ of a suddenly-quenched colloidal liquid of particles interacting through non spherically-symmetric pairwise interactions, whose mean value $\overline{n}(\mathbf{r},Ω,t)$ is constrained to remain uniform and isotropic, $\overline{n}(\mathbf{r},Ω,t)=\overline{n}(t)$. Such self-consistent theory is cast in terms of the time-evolution equation o…
We perform extensive simulations of a binary mixture Lennard-Jones system subjected to a temperature jump in order to study the time evolution of fluctuations during aging. Analyzing data from 1500 different aging realizations, we calculate distributions of inherent structure energies for different aging times and contrast them with equilibrium. We find that the distributions initially become narrower and then widen as the system equilibrates. For deep quenches, fluctuations in the glassy system differ significantly from those observed in equilibrium. Simulation results are partially captured …
While a large number of studies have focused on the nonequilibrium dynamics of a system when it is quenched instantaneously from a disordered phase to an ordered phase, such dynamics have been relatively less explored when the quench occurs at a finite rate. Here we study the slow quench dynamics in two paradigmatic models of classical statistical mechanics, {viz.}, one-dimensional kinetic Ising model and mean-field zero-range process, when the system is annealed slowly to the critical point. Starting from the time evolution equations for the spin-spin correlation function in the Ising model a…
We study numerically the aging properties of the two-dimensional Ising model with quenched disorder considered in our recent paper [Phys. Rev. E 95, 062136 (2017)], where frustration can be tuned by varying the fraction a of antiferromagnetic interactions. Specifically we focus on the scaling properties of the autocorrelation and linear response functions after a quench of the model to a low temperature. We find that the interplay between equilibrium and aging occurs differently in the various regions of the phase diagram of the model. When the quench is made into the ferromagnetic phase the t…
We discuss how to calculate non-equilibrium universal amplitude ratios in the functional renormalization group approach, extending its applicability. In particular, we focus on the critical relaxation of the Ising model with non-conserved dynamics (model A) and calculate the universal amplitude ratio associated with the fluctuation-dissipation ratio of the order parameter, considering a critical quench from a high-temperature initial condition. Our predictions turn out to be in good agreement with previous perturbative renormalization-group calculations and Monte Carlo simulations.
