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Open Access item Systems with two symmetric absorbing states: relating the microscopic dynamics with the macroscopic behavior

Authors:Vázquez, Federico
López, Cristóbal
Keywords:Critical points, Ising model, Magnetisation, Monte Carlo methods, Percolation, Spin dynamics, [PACS] Fluctuation phenomena, random processes, noise, and Brownian motion, [PACS] Phase transitions: general studies, [PACS] Dynamic critical phenomena, [PACS] Ecology and evolution
Issue Date:23-Dec-2008
Publisher:American Physical Society
Citation:Physical Review E 78(6): 061127 (2008)
Abstract:We propose a general approach to study spin models with two symmetric absorbing states. Starting from the microscopic dynamics on a square lattice, we derive a Langevin equation for the time evolution of the magnetization field, that successfully explains coarsening properties of a wide range of nonlinear voter models and systems with intermediate states. We find that the macroscopic behavior only depends on the first derivatives of the spin-flip probabilities. Moreover, an analysis of the mean-field term reveals the three types of transitions commonly observed in these systems—generalized voter, Ising and directed percolation. Monte Carlo simulations of the spin dynamics qualitatively agree with theoretical predictions.
Description:5 pages, 2 figures.-- PACS nrs.: 05.40.-a; 05.70.Fh; 64.60.Ht; 87.23.-n.-- ArXiv pre-print available at: http://arxiv.org/abs/0810.1436
Publisher version (URL):http://dx.doi.org/10.1103/PhysRevE.78.061127
ISSN:1063-651X (Print)
1095-3787 (Online)
Appears in Collections:(IFISC) Artículos

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