Ordering kinetics in q-state clock model: scaling properties and growth laws

Abstract

We present a comprehensive Monte Carlo study of the ordering kinetics in the $d=2$ ferromagnetic $q$-state clock model with nonconserved Glauber dynamics. In agreement with previous studies we find that $q \geqslant 5$ is characterized by two phase transitions occurring at temperatures $T_{c}^1$ and $T_{c}^2$ ($T_{c}^2<T_{c}^1$). Phase ordering kinetics is then investigated by rapidly quenching the system in two phases, in the quasi-long range ordered phase (QLRO) where $T_{c}^2<T<T_{c}^1$ and in the long-range ordered phase (LRO) where $T<T_{c}^2$; $T$ being the quench temperature. Our numerical data for equal time spatial correlation function $C(\textbf{r},t)$ and structure factor $S(k,t)$ support dynamical scaling. Quench in the LRO regime is characterized by a crossover from a preasymptotic growth driven by the annealing of both vortices and interfaces to an interface driven growth at the asymptotic regime with growth exponent $n\simeq 0.5$. In the QLRO quench regime, domains coarsen mainly via annihilation of point defects and our length scale data for $q$ = 9, 12, and 20 suggests a $R(t) \sim (t/\ln t)^{1/2}$ growth law for the $q$-state clock model in the QLRO phase.