Critical relaxation and the combined effects of spatial and temporal boundaries

TL;DR

This paper investigates how spatial and temporal boundaries jointly influence the non-equilibrium critical dynamics of a classical statistical system, revealing complex interplay effects through a perturbative analysis of response functions.

Contribution

It introduces a study of the combined effects of space and time boundaries on critical relaxation, focusing on a semi-infinite $O(n)$-model with dissipative dynamics, without assuming prior scaling forms.

Findings

Determined the short-distance behavior of the response function near boundaries.

Identified non-trivial interplay effects between spatial and temporal boundary conditions.

Provided a perturbative approach that does not assume a specific scaling form.

Abstract

We revisit here the problem of the collective non-equilibrium dynamics of a classical statistical system at a critical point and in the presence of surfaces. The effects of breaking separately space- and time-translational invariance are well understood, hence we focus here on the emergence of a non-trivial interplay between them. For this purpose, we consider a semi-infinite model with $O(n)$-symmetry and purely dissipative dynamics which is prepared in a disordered state and then suddenly quenched to its critical temperature. We determine the short-distance behaviour of its response function within a perturbative approach which does not rely on any a priori assumption on the scaling form of this quantity.