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.

12 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

References in corpus (10)

• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Directed percolation criticality in turbulent liquid crystals
• 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
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• Weakly disordered absorbing-state phase transitions
• Multicritical behavior of the diluted contact process
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Cited by in corpus (10)

• Field-theoretic analysis of directed percolation: Three-loop approximation
• Enhanced rare region effects in the contact process with long-range correlated disorder
• Rare regions and Griffiths singularities at a clean critical point: The five-dimensional disordered contact process
• Emergence of disconnected clusters in heterogeneous complex systems
• Random free-fermion quantum spin chain with multi-spin interactions
• Disordered contact process with asymmetric spreading
• Boundary critical phenomena of the random transverse Ising model in D>=2 dimensions
• 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