Critical ageing of Ising ferromagnets relaxing from an ordered state

Abstract

We investigate the nonequilibrium behaviour 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 are computed up to first order in the ϵ-expansion (ϵ = 4 − d). Ageing behaviour is clearly displayed and the associated universal fluctuation–dissipation ratio tends to for long times. These results are confirmed by Monte Carlo simulations of the two-dimensional Ising model with Glauber dynamics, from which we find . 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.

Publication
J. Stat. Mech.