Spatiotemporal generalization of the Harris criterion and its application to diffusive disorder

We investigate how a clean continuous phase transition is affected by spatiotemporal 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 in the example of model C of the Hohenberg-Halperin classification and comment on Griffiths singularities.

Figure 1

Standard deviation ${\sigma }_{\overline{N}}$ of the number of walkers $N(i,t)$ averaged over a space-time volume of length $L$ and time length $L_t$. The dashed lines represent power laws with exponent $-1/2$ (upper panel) and $-1/4$ (lower panel) and arbitrary prefactors.