Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems (original) (raw)

Fluctuation-dissipation relations in the nonequilibrium critical dynamics of Ising models

Physical Review E, 2003

We investigate the relation between two-time, multi-spin, correlation and response functions in the non-equilibrium critical dynamics of Ising models in d = 1 and d = 2 spatial dimensions. In these non-equilibrium situations, the fluctuation-dissipation theorem (FDT) is not satisfied. We find FDT 'violations' qualitatively similar to those reported in various glassy materials, but quantitatively dependent on the chosen observable, in contrast to the results obtained in infinite-range glass models. Nevertheless, all FDT violations can be understood by considering separately the contributions from large wavevectors, which are at quasi-equilibrium and obey FDT, and from small wavevectors where a generalized FDT holds with a non-trivial fluctuation-dissipation ratio X ∞ . In d = 1, we get X ∞ = 1 2 for spin observables, which measure the orientation of domains, while X ∞ = 0 for observables that are sensitive to the domain-wall motion. Numerical simulations in d = 2 reveal a unique X ∞ ≃ 0.34 for all observables. Measurement protocols for X ∞ are discussed in detail. Our results suggest that the definition of an effective temperature T eff = T /X ∞ for large length scales is generically possible in non-equilibrium critical dynamics. PACS numbers: 05.70.Ln, 75.40.Gb, 75.40.Mg

Relaxation to equilibrium for two dimensional disordered Ising systems in the Griffiths phase

Communications in Mathematical Physics, 1997

We consider Glauber-type dynamics for two dimensional disordered magnets of Ising type. We prove that, if the disorder-averaged influence of the boundary condition is sufficiently small in the equilibrium system, then the corresponding Glauber dynamics is ergodic with probability one and the disorder-average C(t) of time-autocorrelation function satisfies C(t) e −m(log t) 2 (for large t). For the standard two dimensional dilute Ising ferromagnet with i.i.d. random nearest neighbor couplings taking the values 0 or J 0 > 0, our results apply even if the active bonds percolate and J 0 is larger than the critical value J c of the corresponding pure Ising model. For the same model we also prove that in the whole Griffiths' phase the previous upper bound is optimal. This implies the existence of a dynamical phase transition which occurs when J crosses J c .

Fluctuation-dissipation relation in an Ising model without detailed balance

Physical Review E, 2006

We consider the modified Ising model introduced by de Oliveira et al. [J.Phys.A 26, 2317 (1993)], where the temperature depends locally on the spin configuration and detailed balance and local equilibrium are not obeyed. We derive a relation between the linear response function and correlation functions which generalizes the fluctuation-dissipation theorem. In the stationary states of the model, which are the counterparts of the Ising equilibrium states, the fluctuation-dissipation theorem breaks down due to the lack of time reversal invariance. In the non-stationary phase ordering kinetics the parametric plot of the integrated response function χ(t, tw) versus the autocorrelation function is different from that of the kinetic Ising model. However, splitting χ(t, tw) into a stationary and an aging term χ(t, tw) = χst(t − tw) + χag(t, tw), we find χag(t, tw) ∼ t −aχ w f (t/tw), and a numerical value of aχ consistent with aχ = 1/4, as in the kinetic Ising model.

Violation of the fluctuation-dissipation theorem in finite-dimensional spin glasses

Journal of Physics A-mathematical and General, 1998

We study the violation of the fluctuation-dissipation theorem in the three and four dimensional Gaussian Ising spin glasses using on and off equilibrium simulations. We have characterized numerically the function X(C) that determine the violation and we have studied its scaling properties. Moreover we have computed the function x(C) which characterize the breaking of the replica symmetry directly from equilibrium simulations. The two functions are numerically equal and in this way we have established that the conjectured connection between the violation of fluctuation dissipation theorem in the off-equilibrium dynamics and the replica symmetry breaking at equilibrium holds for finite dimensional spin glasses. These results point to a spin glass phase with spontaneously broken replica symmetry in finite dimensional spin glasses.

Numerical approach to metastable states in the zero-temperature random-field Ising model

Physical Review B, 2008

We study numerically the number of single-spin-flip stable states in the T = 0 Random Field Ising Model (RFIM) on random regular graphs of connectivity z = 2 and z = 4 and on the cubic lattice. The annealed and quenched complexities (i.e. the entropy densities) of the metastable states with given magnetization are calculated as a function of the external magnetic field. The results show that the appearance of a (disorder-induced) out-of-equilibrium phase transition in the magnetization hysteresis loop at low disorder can be ascribed to a change in the distribution of the metastable states in the field-magnetization plane.

Stationary Properties of a Randomly Driven Ising Ferromagnet

Physical Review Letters, 1997

We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. Analytic results for the stationary state are presented in mean-field approximation, exhibiting a novel type of first order phase transition related to dynamic freezing. Monte Carlo simulations performed on a quadratic lattice indicate that many features of the mean field theory may survive the presence of fluctuations. 05.50+g 05.70.Jk 64.60Cn 68.35.Rh 75.10.H 82.20.M

Fluctuation effects in the Ising model with reduced interaction and quenched disorder

Physical review. B, Condensed matter, 1996

The effect of quenched random fields and local perturbations of critical temperature on the critical behavior at phase transitions is studied within the framework of an exactly solvable model that takes into account interaction of fluctuations with equal and opposite momenta. Using the replica method the dimensional reduction by 2 for systems with finite-range interaction and quenched random fields is explicitly shown. For interaction of the infinite range the model demonstrates the mean-field critical asymptotics independently of dimensionality or the presence of random fields.

Theory of the Random Field Ising Model

Series on Directions in Condensed Matter Physics, 1997

A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the absence of ferromagnetic order in d ≤ 2 space dimensions for uncorrelated random fields, we consider different random field correlations and in particular the generation of uncorrelated from anti-correlated random fields by thermal fluctuations. In discussing the phase transition, we consider the transition to be characterized by a divergent correlation length and compare the critical exponents obtained from various methods (real space RNG, Monte Carlo calculations, weighted mean field theory etc.). The ferromagnetic transition is believed to be preceded by a spin glass transition which manifests itself by replica symmetry breaking. In the discussion of dynamical properties, we concentrate mainly on the zero temperature depinning transition of a domain wall, which represents a critical point far from equilibrium with new scaling relations and critical exponents.

Fluctuation relations in non-equilibrium stationary states of Ising models

J. Stat. Mech. (2009) P01053, 2009

Fluctuation relations for the entropy production in non equilibrium stationary states of Ising models are investigated by Monte Carlo simulations. Systems in contact with heat baths at two different temperatures or subject to external driving will be studied. In the first case, by considering different kinetic rules and couplings with the baths, the behavior of the probability distributions of the heat exchanged in a time τ with the thermostats, both in the disordered and in the low temperature phase, are discussed. The fluctuation relation is always verified in the large τ limit and deviations from linear response theory are observed. Finite-τ corrections are shown to obey a scaling behavior. In the other case the system is in contact with a single heat bath but work is done by shearing it. Also for this system the statistics collected for the mechanical work shows the validity of the fluctuation relation and preasymptotic corrections behave analogously to the case with two baths.

Dynamical properties of random-field Ising model

Physical Review E, 2013

Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter and the spin-spin correlation functions are studied in the non equilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two dimensional random field Ising model possesses long range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long range order in the system.