Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0312583 · Physical Review Letters

Nonequilibrium Critical Dynamics at Surfaces: Cluster Dissolution and Nonalgebraic Correlations

Michel Pleimling, Ferenc Iglói

Published Apr 7, 2004• 22 citations
arXivHTMLPDF

Abstract

We study nonequilibrium dynamical properties at a free surface after the system is quenched from the high-temperature phase into the critical point. We show that if the spatial surface correlations decay sufficiently rapidly the surface magnetization and/or the surface manifold autocorrelations have a qualitatively different universal short time behavior than the same quantities in the bulk. At a free surface cluster dissolution may take place instead of domain growth, yielding stationary dynamical correlations that decay in a stretched exponential form. This phenomenon takes place in the three-dimensional Ising model and should be observable in real ferromagnets.

DOI
10.1103/physrevlett.92.145701

Related papers

Nonequilibrium critical dynamics in inhomogeneous systems

Michel Pleimling, Ferenc Iglói

We study nonequilibrium dynamical properties of inhomogeneous systems, in particular at a free surface or at a defect plane. Thereby we consider nonconserved (model-A) dynamics of a system which is prepared in the high-temperature phase and quenched into the critical point. Using Monte Carlo simulations we measure single spin relaxation and autocorrelations, as well as manifold autocorrelations and persistence. We show that, depending on the decay of critical static correlations, the short time dynamics can be of two kinds. For slow decay of local correlations the usual domain growth process takes place with nonstationary and algebraic dynamical correlations. If, however, the local correlations decay sufficiently rapidly we have the so-called cluster dissolution scenario, in which case short time dynamical correlations are stationary and have a universal stretched exponential form. This latter phenomenon takes place in the surface of the three-dimensional Ising model and should be observable in real ferromagnets.

arXiv:cond-mat/0410432•Physical Review B•Mar 29, 2005•18 citations

Nonequilibrium Dynamics following a Quench to the Critical Point in a Semi-infinite System

Satya N. Majumdar, Anirvan M. Sengupta

We study the nonequilibrium dynamics (purely dissipative and relaxational) in a semi-infinite system following a quench from the high temperature disordered phase to its critical temperature. We show that the local autocorrelation near the surface of a semi-infinite system decays algebraically in time with a new exponent which is different from the bulk. We calculate this new nonequilibrium surface exponent in several cases, both analytically and numerically.

arXiv:cond-mat/9506050•Physical Review Letters•Mar 25, 1996•18 citations

Re-entrance during nonequilibrium relaxation

László Környei, Michel Pleimling, Ferenc Iglói

We consider nonequilibrium critical dynamics of the two-dimensional Ising model for which the initial state is prepared by switching on random fields with zero mean and variance H . In the initial state there is no magnetic order but the clusters of parallel spins have a percolation transition for small enough H . Using heat-bath dynamics we measure the relaxation of the magnetization which shows a re-entrance in time. Due to cluster dissolution in the early time regime there is a decrease of the magnetization, followed by an increase due to nonequilibrium domain growth which itself turns to a decrease due to equilibrium relaxation. The power law decay of the nonequilibrium autocorrelation function is not influenced by the percolation in the initial state.

arXiv:cond-mat/0509372•Europhysics Letters (EPL)•Dec 13, 2005•4 citations

Persistence of Manifolds in Nonequilibrium Critical Dynamics

Satya N. Majumdar, Alan J. Bray

We study the persistence probability $P(t)$ that, starting from a random initial condition, the magnetization of a ${d}^{\ensuremath{'}}$-dimensional manifold of a $d$-dimensional spin system at its critical point does not change sign up to time $t$. For ${d}^{\ensuremath{'}}>0$ we find three distinct late-time decay forms for $P(t)$: exponential, stretched exponential, and power law, depending on a single parameter $\ensuremath{\zeta}=(D\ensuremath{-}2+\ensuremath{\eta})/z$, where $D=d\ensuremath{-}{d}^{\ensuremath{'}}$ and $\ensuremath{\eta},z$ are standard critical exponents. In particular, we predict that for a line magnetization in the critical $d=2$ Ising model, $P(t)$ decays as a power law while, for $d=3$, $P(t)$ decays as a power of $t$ for a plane magnetization but as a stretched exponential for a line magnetization. Numerical results are consistent with these predictions.

arXiv:cond-mat/0302537•Physical Review Letters•Jul 18, 2003•27 citations

Critical nonequilibrium cluster-flip relaxations in Ising models

Yusuke Tomita, Yoshihiko Nonomura

We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the stretched-exponential function, we find that the dynamics changes from the stretched exponential to the power function as the dimensionality is increased: The two-, three-, four-, and infinite-dimensional Ising models are numerically studied, and the four- and infinite-dimensional Ising models exhibit the power-law relaxation. We also show that the finite-size scaling analysis using the normalized correlation length is markedly effective for the analysis of relaxational processes rather than the direct use of the Monte Carlo step.

arXiv:1808.07761•Physical review. E•Nov 12, 2018•5 citations

Spin Systems far from Equilibrium: Aging and Dynamic Phase Transition

Hyunhang Park

Among the many non-equilibrium processes encountered in nature we deal with two different but related aspects. One is the non-equilibrium relaxation process that is at the origin of \'aging phenomena••, and the other one is a non-equilibrium phase transition, called ••dynamic phase transition••. One of the main purposes of our research is to explore more realistic situations than studied previously. Indeed, in the study of aging phenomena certain kinds of disorder effects are considered, and we introduce the ••surface•• as a spatial boundary to the system undergoing the dynamic phase transition. In order to observe these processes as clearly as possible, we study in both cases simple spin systems. Using Monte Carlo simulations we first investigate aging in three-dimensional Ising spin glasses as well as in two-dimensional Ising models with disorder quenched to low temperatures. The time-dependent dynamical correlation length L(t) is determined numerically and the scaling behavior of various two-time quantities as a function of L(t)/L(s) is discussed where t and s are two different times. For disordered Ising models deviations of L(t) from algebraic growth law show up. The generalized scaling forms as a function of L(t)/L(s) reveal a generic simple aging scenario for Ising spin glasses as well as for disordered Ising ferromagnets. We also study the local critical phenomena at a dynamic phase transition by means of numerical simulations of kinetic Ising models with surfaces subjected to a periodic oscillating field. We examine layer-dependent quantities, such as the period-averaged magnetization per layer Q(z) and the layer susceptibility ¥ö(z), and determine local critical exponents through finite size scaling. Both for two and three dimensions, we find that the values of the surface exponents differ from those of the equilibrium critical surface. It is revealed that the surface phase diagram of the non-equilibrium system is not identical to that of the equilibrium system in three dimensions.

•Mar 22, 2013•0 citations
We study nonequilibrium dynamical properties at a free surface after the system is quenched from the high-temperature phase into the critical point. We show that if the spatial surface correlations decay sufficiently rapidly the surface magnetization and/or the surface manifold autocorrelations have a qualitatively different universal short time behavior than the same quantities in the bulk. At a free surface cluster dissolution may take place instead of domain growth, yielding stationary dynamical correlations that decay in a stretched exponential form. This phenomenon takes place in the three-dimensional Ising model and should be observable in real ferromagnets.
We study nonequilibrium dynamical properties of inhomogeneous systems, in particular at a free surface or at a defect plane. Thereby we consider nonconserved (model-A) dynamics of a system which is prepared in the high-temperature phase and quenched into the critical point. Using Monte Carlo simulations we measure single spin relaxation and autocorrelations, as well as manifold autocorrelations and persistence. We show that, depending on the decay of critical static correlations, the short time dynamics can be of two kinds. For slow decay of local correlations the usual domain growth process takes place with nonstationary and algebraic dynamical correlations. If, however, the local correlations decay sufficiently rapidly we have the so-called cluster dissolution scenario, in which case short time dynamical correlations are stationary and have a universal stretched exponential form. This latter phenomenon takes place in the surface of the three-dimensional Ising model and should be observable in real ferromagnets.
We consider nonequilibrium critical dynamics of the two-dimensional Ising model for which the initial state is prepared by switching on random fields with zero mean and variance H . In the initial state there is no magnetic order but the clusters of parallel spins have a percolation transition for small enough H . Using heat-bath dynamics we measure the relaxation of the magnetization which shows a re-entrance in time. Due to cluster dissolution in the early time regime there is a decrease of the magnetization, followed by an increase due to nonequilibrium domain growth which itself turns to a decrease due to equilibrium relaxation. The power law decay of the nonequilibrium autocorrelation function is not influenced by the percolation in the initial state.
We study the persistence probability P(t)P(t)P(t) that, starting from a random initial condition, the magnetization of a ${d}^{\ensuremath{'}}$-dimensional manifold of a ddd-dimensional spin system at its critical point does not change sign up to time ttt. For ${d}^{\ensuremath{'}}>0$ we find three distinct late-time decay forms for P(t)P(t)P(t): exponential, stretched exponential, and power law, depending on a single parameter $\ensuremath{\zeta}=(D\ensuremath{-}2+\ensuremath{\eta})/z$, where $D=d\ensuremath{-}{d}^{\ensuremath{'}}$ and $\ensuremath{\eta},z$ are standard critical exponents. In particular, we predict that for a line magnetization in the critical d=2d=2d=2 Ising model, P(t)P(t)P(t) decays as a power law while, for d=3d=3d=3, P(t)P(t)P(t) decays as a power of ttt for a plane magnetization but as a stretched exponential for a line magnetization. Numerical results are consistent with these predictions.
We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the stretched-exponential function, we find that the dynamics changes from the stretched exponential to the power function as the dimensionality is increased: The two-, three-, four-, and infinite-dimensional Ising models are numerically studied, and the four- and infinite-dimensional Ising models exhibit the power-law relaxation. We also show that the finite-size scaling analysis using the normalized correlation length is markedly effective for the analysis of relaxational processes rather than the direct use of the Monte Carlo step.
Among the many non-equilibrium processes encountered in nature we deal with two different but related aspects. One is the non-equilibrium relaxation process that is at the origin of \'aging phenomena••, and the other one is a non-equilibrium phase transition, called ••dynamic phase transition••. One of the main purposes of our research is to explore more realistic situations than studied previously. Indeed, in the study of aging phenomena certain kinds of disorder effects are considered, and we introduce the ••surface•• as a spatial boundary to the system undergoing the dynamic phase transition. In order to observe these processes as clearly as possible, we study in both cases simple spin systems. Using Monte Carlo simulations we first investigate aging in three-dimensional Ising spin glasses as well as in two-dimensional Ising models with disorder quenched to low temperatures. The time-dependent dynamical correlation length L(t) is determined numerically and the scaling behavior of various two-time quantities as a function of L(t)/L(s) is discussed where t and s are two different times. For disordered Ising models deviations of L(t) from algebraic growth law show up. The generalized scaling forms as a function of L(t)/L(s) reveal a generic simple aging scenario for Ising spin glasses as well as for disordered Ising ferromagnets. We also study the local critical phenomena at a dynamic phase transition by means of numerical simulations of kinetic Ising models with surfaces subjected to a periodic oscillating field. We examine layer-dependent quantities, such as the period-averaged magnetization per layer Q(z) and the layer susceptibility ¥ö(z), and determine local critical exponents through finite size scaling. Both for two and three dimensions, we find that the values of the surface exponents differ from those of the equilibrium critical surface. It is revealed that the surface phase diagram of the non-equilibrium system is not identical to that of the equilibrium system in three dimensions.