Correlations and coarsening in the q-state Potts model.

Abstract

We study the nonequilibrium dynamics of the $q$-state Potts model following a quench from the high-temperature disordered phase to zero temperature. We calculate, within a Gaussian closure approximation, the time-dependent two-point correlation functions for general $q$. These correlation functions obey dynamic scaling with a length scale $L(t)\ensuremath{\sim}{t}^{1/2}$, while the autocorrelation function decays as $L(t{)}^{\ensuremath{-}\ensuremath{\lambda}(q)}$. We also establish a correspondence of this model to the Ising model evolving with a fixed magnetization $(2/q\ensuremath{-}1)$. Extensive numerical simulations of the Potts model in two dimensions show good agreement with our theory.