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

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.