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From micro to macro in systems with two symmetric absorbing states

By Federico Vazquez, Cristobal Lopez and Maxi San Miguel
XVI Congreso de Fisica Estadistica, Huelva, 2009 - 09 - 10/12 2009

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.