Rare regions and Griffiths singularities at a clean critical point: The five-dimensional disordered contact process

TL;DR

This study examines the disordered contact process in five dimensions, revealing mean-field critical behavior with Griffiths singularities, and resolves contradictions between theoretical predictions and observed phenomena through simulations.

Contribution

It demonstrates that the five-dimensional disordered contact process exhibits mean-field critical behavior with Griffiths singularities, clarifying the role of disorder and rare regions at the critical point.

Findings

Critical behavior is mean-field type.

Griffiths singularities with finite dynamical exponent.

Simulation of systems with up to 70^5 sites confirms theory.

Abstract

We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type, i.e., identical to that of the clean five-dimensional contact process. It is accompanied by off-critical power-law Griffiths singularities whose dynamical exponent $z'$ saturates at a finite value as the transition is approached. These findings resolve the apparent contradiction between the Harris criterion which implies that weak disorder is renormalization-group irrelevant and the rare-region classification which predicts unconventional behavior. We confirm and illustrate our theory by large-scale Monte-Carlo simulations of systems with up to $70^5$ sites. We also relate our results to a recently established general relation between the Harris criterion and Griffiths singularities [Phys. Rev. Lett. {\bf 112}, 075702 (2014)], and we discuss implications for other phase transitions.