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We investigate how a clean continuous phase transition is affected byspatio-temporal disorder, i.e., by an external perturbation that fluctuates inboth space and time. We derive a generalization of the Harris criterion for thestability of the clean critical behavior in terms of the space-time correlationfunction of the external perturbation. As an application, we consider diffusivedisorder, i.e, an external perturbation governed by diffusive dynamics, and itseffects on a variety of equilibrium and nonequilibrium critical points. We alsodiscuss the relation between diffusive disorder and diffusive dynamical degreesof freedom on the example of model C of the Hohenberg-Halperin classification,and we comment on Griffiths singularities.

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