Kinetics of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Q</mml:mi></mml:math>-State Potts Model in Two Dimensions

Abstract

An efficient Monte Carlo procedure is applied to the study of the kinetics of low-and high-$Q$-state Potts models quenched from an initial high-temperature ($T\ensuremath{\gg}{T}_{c}$) state to very low temperatures ($T\ensuremath{\simeq}0$). After an initial transient period, the mean domain size, $R$, increases algebraically with time as $R\ensuremath{\sim}C{t}^{n}$. The exponent $n$ decreases from \textonehalf{} for $Q=2$ (Ising model) to 0.38 for large $Q$. The change in $n$ is attributed to a coalescence process which becomes increasingly effective with decreasing $Q$. For large $Q$, the prefactor $C$ is proportional to ${Q}^{\frac{1}{2}}$.