Simulating the contact process in heterogeneous environments

S. V. Fallert, J. J. Ludlam, and S. N. Taraskin
Phys. Rev. E 77, 051125 – Published 23 May 2008

Abstract

The one-dimensional contact process (CP) in a heterogeneous environment—a binary chain consisting of two types of site with different recovery rates—is investigated. It is argued that the commonly used random-sequential Monte Carlo simulation method which employs a discrete notion of time is not faithful to the rates of the contact process in a heterogeneous environment. Therefore, a modification of this algorithm along with two alternative continuous-time implementations are analyzed. The latter two are an adapted version of the n-fold way used in Ising model simulations and a method based on a modified priority queue. It is demonstrated that the commonly used (but incorrect as we believe) discrete-time method yields a different critical threshold from all other algorithms considered. Finite-size scaling of the lowest gap in the spectrum of the Liouville time-evolution operator for the CP gives an estimate of the critical rate which supports these findings. Further, a performance test indicates an advantage in using the continuous-time methods in systems with heterogeneous rates. This result promises to help in the analysis of the CP in disordered systems with heterogeneous rates in which simulation is a challenging task due to very long relaxation times.

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  • Received 10 September 2007

DOI:https://doi.org/10.1103/PhysRevE.77.051125

©2008 American Physical Society

Authors & Affiliations

S. V. Fallert*

  • Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom

J. J. Ludlam

  • Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom

S. N. Taraskin

  • St. Catharine’s College and Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom

  • *sf287@cam.ac.uk

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Issue

Vol. 77, Iss. 5 — May 2008

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