From microscopic to macroscopic dynamics in systems with two symmetric absorbing states

In this talk, I will present a general approach to study spin
systems with two symmetric absorbing states. I will first give a short
introduction on interacting particle systems, showing some of the most
common
examples that probability theorists have investigated, and then I will
focus on a subset of them, spin models. Starting from the microscopic
dynamics on a square lattice, it is possible to derive a Langevin
equation for
the time evolution of the magnetization field, that explains coarsening
properties of a wide range of nonlinear voter models. It turns out that
the macroscopic behavior only depends on the first derivatives of the
spin-flip probabilities. To illustrate these results, I apply this
approach to
study models with intermediate states. Finally, I show how a mean-field
approximation reveals the three types of transitions commonly observed in
these systems -generalized voter, Ising and directed percolation-.