Scaling Exponent for Coarsening in a 1D q-state system

Abstract

An exponent $β$ which characterises non-equilibrium coarsening processes is calculated in a deterministic solvable model of coarsening for a 1D q-state Potts system. We study how the fraction of sites P which have never changed their state, scale with the characteristic domain length $<\ell>$. $β$ is defined by P \sim $<\ell>^{β-1}$. We propose a new model of coarsening that prevents correlations from developing between domains thereby ensuring tractability and an exact result for any q.