Aging in ferromagnetic ordering: full decay and finite-size scaling of autocorrelation

Abstract

Nonequilibrium dynamics in Ising and Ginzburg–Landau models were studied for a nonconserved order parameter that mimics ordering in ferromagnets. The focus was on the understanding of the decay of the two time (t, tw; t > tw) order-parameter correlation function. For this quantity, a full form has been obtained empirically which, for t ≫ tw, provides a power-law ∼ (ℓ/ℓw)−λ, ℓ and ℓw being the characteristic lengths at t and tw, respectively. This empirical form was used for a finite-size scaling analysis to obtain the exponent λ in space dimensions d = 2 and 3. Our estimates of λ and understanding of the finite-size effects, for the models considered, provide useful information on the relevance of thermal noise. The values of λ obtained are in good agreement with the predictions of a theory based on Gaussian auxiliary field ansatz.