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 705 sites. We also relate our results to a recently established general relation between the Harris criterion and Griffiths singularities [Phys. Rev. Lett. 112, 075702 (2014)PRLTAO0031-900710.1103/ PhysRevLett.112.075702], and we discuss implications for other phase transitions.



Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Condensed Matter Physics; Physics; Critical Behavior; Dynamical Exponents; General Relations; Griffiths Singularities; Nonequilibrium Phase Transitions; Optimal Fluctuation; Other Phase Transitions; Renormalization Group; Monte Carlo Methods; Monte Carlo Method; Phase Transition; Monte Carlo Method; Phase Transition

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2014 American Physical Society (APS), All rights reserved.

Publication Date

01 Jul 2014