Collective non-equilibrium dynamics at surfaces and the spatio-temporal edge

TL;DR

This paper investigates the complex non-equilibrium behavior at the intersection of spatial surfaces and temporal boundaries in the classical Ising model, revealing universal scaling features through numerical and theoretical analysis.

Contribution

It uncovers new universal phenomena at the spatio-temporal edge of non-equilibrium systems, combining numerical simulations with a field-theoretical framework.

Findings

Universal scaling regime at the spatio-temporal edge

Numerical evidence of edge effects in the Ising model

Field-theoretical explanation of observed phenomena

Abstract

Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical systems, which hold at a coarse-grained scale in equilibrium and are broken by spatial and temporal boundaries, the former being implemented by surfaces - unavoidable in real samples - the latter by some initial condition for the dynamics which causes a non-equilibrium evolution. While the separate effects of these two boundaries are well understood, we demonstrate here that additional, unexpected features arise upon approaching the effective edge formed by their intersection. For this purpose, we focus on the classical semi-infinite Ising model with spin-flip dynamics evolving out of equilibrium at its critical point. Considering both subcritical and critical values of the coupling among surface spins, we present numerical evidence of a scaling regime with universal features which emerges upon approaching the spatio-temporal edge and we rationalise these findings within a field-theoretical approach.