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.



Keywords and Phrases

Absorbing-state transitions; Contact process; Critical behavior; Critical points; Directed percolation; Disorder strength; Disordered system; Dynamical scaling; Griffiths phase; Infinite time; Monte Carlo Simulation; Power-law; Quenched randomness; Spatial disorder; Three dimensions; Three-dimensional contact; Universality class; Random processes

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Document Type

Article - Journal

Document Version

Final Version

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© 2012 American Physical Society (APS), All rights reserved.

Publication Date

01 Nov 2012

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Physics Commons