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

Details Systems with two symmetric absorbing states: relating the microscopic dynamics with the macroscopic behavior Systems with two symmetric absorbing states: relating the microscopic dynamics with the macroscopic behavior

2008-10-08

arxiv.org/abs/0810.1436v1

Phys. Rev. E 78, 061127 (2008)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 2 figures

Scientific paper

10.1103/PhysRevE.78.061127

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.

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