A far-from-equilibrium fluctuation-dissipation relation for an Ising-Glauber-like model

TL;DR

This paper derives an exact, general fluctuation-dissipation relation for an Ising-Glauber-like model, applicable far from equilibrium, and demonstrates its use in studying aging in a 2D ferromagnetic system.

Contribution

It provides a novel exact response function expression for Ising-Glauber models with arbitrary couplings, extending fluctuation-dissipation relations beyond equilibrium.

Findings

Derived an exact response function in terms of thermodynamic averages.

Implemented a discrete-time version in Monte Carlo simulations.

Analyzed aging behavior in the 2D ferromagnetic Ising-Glauber model.

Abstract

We derive an exact expression of the response function to an infinitesimal magnetic field for an Ising-Glauber-like model with arbitrary exchange couplings. The result is expressed in terms of thermodynamic averages and does not depend on the initial conditions or on the dimension of the space. The response function is related to time-derivatives of a complicated correlation function and so the expression is a generalisation of the equilibrium fluctuation-dissipation theorem in the special case of this model. Correspondence with the Ising-Glauber model is discussed. A discrete-time version of the relation is implemented in Monte Carlo simulations and then used to study the aging regime of the ferromagnetic two-dimensional Ising-Glauber model quenched from the paramagnetic phase to the ferromagnetic one. Our approach has the originality to give direct access to the response function and the fluctuation-dissipation ratio.