Spatio-temporal generalization of the Harris criterion and its application to diffusive disorder

TL;DR

This paper generalizes the Harris criterion to spatio-temporal disorder, analyzing its impact on phase transitions, especially with diffusive disorder, and explores implications for critical points and Griffiths singularities.

Contribution

It introduces a generalized Harris criterion based on space-time correlations and applies it to diffusive disorder affecting various critical phenomena.

Findings

Diffusive disorder can destabilize certain critical points.

The generalized criterion predicts stability thresholds for phase transitions.

Connections between diffusive disorder and dynamical degrees of freedom are established.

Abstract

We investigate how a clean continuous phase transition is affected by spatio-temporal disorder, i.e., by an external perturbation that fluctuates in both space and time. We derive a generalization of the Harris criterion for the stability of the clean critical behavior in terms of the space-time correlation function of the external perturbation. As an application, we consider diffusive disorder, i.e, an external perturbation governed by diffusive dynamics, and its effects on a variety of equilibrium and nonequilibrium critical points. We also discuss the relation between diffusive disorder and diffusive dynamical degrees of freedom on the example of model C of the Hohenberg-Halperin classification, and we comment on Griffiths singularities.