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

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.