Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench

TL;DR

This paper investigates the autocorrelation behavior of conserved spin systems after a critical quench, deriving theoretical predictions and confirming them with numerical simulations for the Ising model.

Contribution

It introduces a new scaling form for the autocorrelation function in conserved spin systems and verifies it through simulations and theoretical analysis.

Findings

Autocorrelation scales with the correlation length as predicted.

The exponent  is found to be d+2 in the nd7 limit.

Numerical results for the Ising model agree with the theoretical predictions.

Abstract

We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t)\sim t^{1/z}, we find that for times t' and t satisfying L(t') << L(t) << L(t')^\phi well inside the scaling regime, the spin autocorrelation function behaves like <s(t)s(t')> = L(t')^{-(d-2+\eta)} [L(t')/L(t)]^{\lambda_c}. For the O(n) model in the n -> \infty limit, we show that \lambda_c=d+2 and \phi=z/2. We give a heuristic argument suggesting that this result is in fact valid for any dimension d and spin vector dimension n. We present numerical simulations for the conserved Ising model in d=1 and d=2, which are fully consistent with the present theory.