Rare Regions and Griffiths Singularities at a Clean Critical Point: The Five-Dimensional Disordered Contact Process
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.
T. Vojta et al., "Rare Regions and Griffiths Singularities at a Clean Critical Point: The Five-Dimensional Disordered Contact Process," Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 90, no. 1, American Physical Society (APS), Jul 2014.
The definitive version is available at https://doi.org/10.1103/PhysRevE.90.012139
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)
Article - Journal
© 2014 American Physical Society (APS), All rights reserved.
01 Jul 2014