Finite-size scaling in the ageing dynamics of the $1D$ Glauber-Ising model

TL;DR

This paper provides an exact analysis of finite-size scaling in the non-equilibrium ageing dynamics of the 1D Glauber-Ising model after a zero-temperature quench, highlighting the behavior of correlators in finite systems.

Contribution

It introduces an analytical continuation technique to compute correlators exactly in finite 1D Glauber-Ising chains, confirming finite-size scaling in non-equilibrium dynamics.

Findings

Finite-size scaling confirmed in non-equilibrium dynamics.

Exact computation of correlators using analytical continuation.

Behavior of the plateau height $C_{ ext{infty}}^{(2)}$ analyzed.

Abstract

Single-time and two-time correlators are computed exactly in the $1D$ Glauber-Ising model after a quench to zero temperature and on a periodic chain of finite length $N$, using a simple analytical continuation technique. Besides the general confirmation of finite-size scaling in non-equilibrium dynamics, this allows to test the scaling behaviour of the plateau height $C_{\infty}^{(2)}$ to which the two-time auto-correlator converges, when deep into the finite-size regime.