We studied the nonequilibrium aging behavior of the Random Field Ising Model in three dimensions for various values of the disorder strength. This allowed us to investigate how the aging behavior changes across the ferromagnetic-paramagnetic phase transition. We investigated a large system size of $N=256^3$ spins and up to $10^8$ Monte Carlo sweeps. To reach these necessary long simulation times we employed an implementation running on Intel Xeon Phi coprocessors, reaching single spin flip times as short as 6 ps. We measured typical correlation functions in space and time to extract a growing length scale and corresponding exponents.
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 employ Monte Carlo simulations to study the non-equilibrium relaxation of driven Ising lattice gases in two dimensions. Whereas the temporal scaling of the density auto-correlation function in the non-equilibrium steady state does not allow a precise measurement of the critical exponents, these can be accurately determined from the aging scaling of the two-time auto-correlations and the order parameter evolution following a quench to the critical point. We obtain excellent agreement with renormalization group predictions based on the standard Langevin representation of driven Ising lattice …
The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the two-dimensional Ising model with power-law long-range interactions is studied via Monte Carlo simulations. The dynamical scaling of the two-time spin-spin autocorrelator is well described by simple aging for all interaction ranges studied. The autocorrelation exponents are consistent with $λ=1.25$ in the effectively short-range regime, while for stronger long-range in…
We study numerically the phase-ordering kinetics of the two-dimensional site-diluted Ising model. The data can be interpreted in a framework motivated by renormalization-group concepts. Apart from the usual fixed point of the non-diluted system, there exist two disorder fixed points, characterized by logarithmic and power-law growth of the ordered domains. This structure gives rise to a rich scaling behavior, with an interesting crossover due to the competition between fixed points, and violation of superuniversality.
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 $…
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）
Behavior of two-time autocorrelation during the phase separation in solid binary mixtures are studied via numerical solutions of the Cahn-Hilliard equation as well as Monte Carlo simulations of the Ising model. Results are analyzed via state-of-the-art methods, including the finite-size scaling technique. Full forms of the autocorrelation in space dimensions $2$ and $3$ are obtained empirically. The long time behavior are found to be power-law type, with exponents unexpectedly higher than the ones for the ferromagnetic ordering. Both Chan-Hilliard and Ising models provide results consistent wi…
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…
Deviations from Full Aging in Numerical Spin Glass Models
完全或纯老化行为的偏差，即老化玻璃体系的相关和响应函数的完美$t/t_w$标度，在理论上还没有得到很好的理解。Rodriguez等人（Phys. Rev. Lett. 91，037203（2003））已经表明，在初始淬火期间，在无限冷却速率的极限下，完全老化适用于热致磁化。在数值模型中，瞬时热猝灭可以-并且通常-应用。这激发了目前的数值研究的Edwards-AndersonIsing自旋玻璃模型的老化行为的短期和长期的高斯相互作用，分别。我们采样的分布在适当定义的亚稳态谷进入年龄$t_w$的停留时间$t$，发现从$t/t_w$缩放的偏差是小的，系统地减少系统的大小的增长和/或温度降低。最后，讨论了这种行为与关联函数本身的标度之间的联系。
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…
We study the out-of-equilibrium aging dynamics of the Random Energy Model (REM) ruled by a single spin-flip Metropolis dynamics. We focus on the dynamical evolution taking place on time-scales diverging with the system size. Our aim is to show to what extent the activated dynamics displayed by the REM can be described in terms of an effective trap model. We identify two time regimes: the first one corresponds to the process of escaping from a basin in the energy landscape and to the subsequent exploration of high energy configurations, whereas the second one corresponds to the evolution from a…
The time distribution of relaxation events in an aging system is investigated via molecular dynamics simulations. The focus is on the distribution functions of the first passage time, $p_1(Δt)$, and the persistence time, $p(τ)$. In contrast to previous reports, both $p_1$ and $p$ are found to evolve with time upon aging. The age dependence of the persistence time distribution is shown to be sensitive to the details of the algorithm used to extract it from particle trajectories. By updating the reference point in event detection algorithm and accounting for the event specific aging time, we unc…
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…
We investigate the dynamic relaxation of random walks on temporal networks by focusing in the recently proposed activity driven model [Perra \textit{et al.} Sci. Rep. srep00469 (2012)]. For realistic activity distributions with a power-law form, we observe the presence of a very slow relaxation dynamics compatible with aging effects. A theoretical description of this processes in achieved by means of a mapping to Bouchaud's trap model. The mapping highlights the profound difference in the dynamics of the random walks according to the value of the exponent $γ$ in the activity distribution.
We study phase ordering dynamics in the three-dimensional nearest-neighbor Ising model, following rapid quenches from infinite to zero temperature. Results on various aspects, viz., domain growth, persistence, aging and pattern, have been obtained via the Glauber Monte Carlo simulations of the model on simple cubic lattice. These are analyzed via state-of-the-art methods, including the finite-size scaling, and compared with those for quenches to a temperature above the roughening transition. Each of these properties exhibit remarkably different behavior at the above mentioned final temperature…
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process in which successive events are separated by scale-free waiting time periods. Among other ubiquitous long time properties, this process exhibits aging: events counted initially in a time interval [0,t] statistically strongly differ from those observed at later times [t_a,t_a+t]. In complex, disordered media, processes with scale-free waiting times play a part…
We use large-scale Monte Carlo simulations to obtain comprehensive results for domain growth and aging in the random field XY model in dimensions $d=2,3$. After a deep quench from the paramagnetic phase, the system orders locally via annihilation of topological defects, i.e., vortices and anti-vortices. The evolution morphology of the system is characterized by the correlation function and the structure factor of the magnetization field. We find that these quantities obey dynamical scaling, and their scaling function is independent of the disorder strength $Δ$. However, the scaling form of the…
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…
Complex systems are often inherently non-ergodic and non-Markovian for which Shannon entropy loses its applicability. In particular accelerating, path-dependent, and aging random walks offer an intuitive picture for these non-ergodic and non-Markovian systems. It was shown that the entropy of non-ergodic systems can still be derived from three of the Shannon-Khinchin axioms, and by violating the fourth -- the so-called composition axiom. The corresponding entropy is of the form $S_{c,d} \sim \sum_i Γ(1+d,1-c\ln p_i)$ and depends on two system-specific scaling exponents, $c$ and $d$. This entro…
In this paper, we explore the reduction of functionality in a complex system as a consequence of cumulative random damage and imperfect reparation, a phenomenon modeled as a dynamical process on networks. We analyze the global characteristics of the diffusive movement of random walkers on networks where the walkers hop considering the capacity of transport of each link. The links are susceptible to damage that generates bias and aging. We describe the algorithm for the generation of damage and the bias in the transport producing complex eigenvalues of the transition matrix that defines the ran…
