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

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 $z^{\prime }$ 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.

10 pages, 5 eps figures included, applies the optimal fluctuation theory of arXiv:1309.0753 to the contact process

References in corpus (10)

• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
• Infinite-randomness critical point in the two-dimensional disordered contact process
• Quantum Griffiths effects in itinerant Heisenberg magnets
• Critical behavior and Griffiths effects in the disordered contact process
• Effects of dissipation on a quantum critical point with disorder
• Infinite-randomness quantum critical points induced by dissipation
• Weakly disordered absorbing-state phase transitions
• Monte-Carlo simulations of the clean and disordered contact process in three dimensions
• Finite-size scaling of directed percolation in the steady state

Cited by in corpus (4)

• Long-range epidemic spreading in a random environment
• Pre-asymptotic critical behavior and effective exponents in disordered metallic quantum ferromagnets
• Localization transition, Lifschitz tails and rare-region effects in network models
• Enhanced rare region effects in the contact process with long-range correlated disorder