Monte-Carlo simulations of the clean and disordered contact process in three dimensions

Abstract

The absorbing-state transition in the three-dimensional contact process with and without quenched randomness is investigated by means of Monte-Carlo simulations. In the clean case, a reweighting technique is combined with a careful extrapolation of the data to infinite time to determine with high accuracy the critical behavior in the three-dimensional directed percolation universality class. In the presence of quenched spatial disorder, our data demonstrate that the absorbing-state transition is governed by an unconventional infinite-randomness critical point featuring activated dynamical scaling. The critical behavior of this transition does not depend on the disorder strength, i.e., it is universal. Close to the disordered critical point, the dynamics is characterized by the nonuniversal power laws typical of a Griffiths phase. We compare our findings to the results of other numerical methods, and we relate them to a general classification of phase transitions in disordered systems based on the rare region dimensionality.

arXiv comment12 pages, 11 eps figures included, applies simulation and data analysis techniques developed in arXiv:0810.1569 to the 3D contact process, final version as published

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• Contact process with simultaneous spatial and temporal disorder
• Quantum critical behavior of diluted quasi-one-dimensional Ising chains
• Effects of lattice dilution on the non-equilibrium phase transition in the stochastic Susceptible-Infectious-Recovered model