Non-equilibrium relaxations: ageing and finite-size effects

TL;DR

This paper investigates the long-time relaxation behavior of spin systems during phase-ordering in finite geometries, proposing a scaling approach validated by exact solutions in the spherical model across dimensions 3 and 4.

Contribution

It introduces a phenomenological finite-size scaling ansatz for non-equilibrium relaxations, supported by exact solutions in the kinetic spherical model.

Findings

Finite-size effects significantly influence aging dynamics.

The proposed scaling ansatz accurately describes the relaxation behavior.

Results are validated in dimensions 3 and 4.

Abstract

The long-time behaviour of spin-spin correlators in the slow relaxation of systems undergoing phase-ordering kinetics is studied in geometries of finite size. A phenomenological finite-size scaling ansatz is formulated and tested through the exact solution of the kinetic spherical model, quenched to below the critical temperature, in $2<d<4$ dimensions.