Critical aging of Ising ferromagnets relaxing from an ordered state

TL;DR

This paper studies the universal aging behavior of the critical relaxation in the d-dimensional Ising model, deriving scaling forms and fluctuation-dissipation ratios using field theory and confirming results with Monte Carlo simulations.

Contribution

It provides the first derivation of universal scaling functions and fluctuation-dissipation ratios for aging in critical Ising models during relaxation from an ordered state.

Findings

Universal scaling forms of response and correlation functions derived

Fluctuation-dissipation ratio computed up to first order in epsilon-expansion

Monte Carlo simulations confirm theoretical predictions

Abstract

We investigate the nonequilibrium behavior of the d-dimensional Ising model with purely dissipative dynamics during its critical relaxation from a magnetized initial configuration. The universal scaling forms of the two-time response and correlation functions of the magnetization are derived within the field-theoretical approach and the associated scaling functions and fluctuation-dissipation ratio are computed up to first order in the epsilon-expansion. Aging behavior is clearly displayed during the critical relaxation. These results are confirmed by Monte Carlo simulations of the two-dimensional Ising model with Glauber dynamics. The crossover to the case of relaxation from a disordered state is discussed and the crossover function for the fluctuation-dissipation ratio is computed within the Gaussian approximation.