Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models

TL;DR

This paper studies how fluctuation-dissipation relations behave in the non-equilibrium critical dynamics of Ising models, revealing observable-dependent violations and proposing a generalized fluctuation-dissipation ratio.

Contribution

It demonstrates the observable dependence of FDT violations and introduces a generalized FDT with a non-trivial ratio in non-equilibrium Ising models.

Findings

FDT violations depend on the observable in non-equilibrium dynamics.

A generalized FDT with a non-trivial ratio X is applicable at small wavevectors.

Numerical simulations show a universal X = 0.34 in 2D Ising models.

Abstract

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 limit 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 Teff = T / X for large length scales is generically possible in non-equilibrium critical dynamics.