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 $q⩾5$ 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 $C(\text{r},t)$ 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.

References in corpus (15)

• Theory of Phase Ordering Kinetics
• Growth Laws for Phase Ordering
• Probability-Changing Cluster Algorithm for Two-Dimensional XY and Clock Models
• Universality away from critical points in two-dimensional phase transitions
• Coarsening in the q-State Potts Model and the Ising Model with Globally Conserved Magnetization
• Probability-Changing Cluster Algorithm for Potts Models
• Finite-size Scaling of Correlation Ratio and Generalized Scheme for the Probability-Changing Cluster Algorithm
• Non-Kosterlitz-Thouless transitions for the $q$-state clock models
• Numerical study of the phase transitions in the two-dimensional Z(5) vector model
• Scaling and universality in the aging kinetics of the two-dimensional clock model
• Kosterlitz-Thouless transition in planar spin models with bond dilution
• True and quasi long-range order in the generalized $q$-state clock model
• Comment on `Six-state clock model on the square lattice: Fisher zero approach with Wang-Landau sampling'
• The phase transitions in 2D Z(N) vector models for N>4
• Phase Ordering Dynamics in the Continuum q-state Clock Model

Cited by in corpus (11)

• Critical properties of the two-dimensional $q$-state clock model
• Accurate simulation of q-state clock model
• Monte Carlo study of duality and the Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional $q$-state clock model in flow representations
• Clock model interpolation and symmetry breaking in O(2) models
• Cross derivative: a universal and efficient method for phase transitions in classical spin models
• Probing phase transitions with correlations in configuration space
• Ordering kinetics in the active Ising model
• Consequence of anisotropy on flocking: the discretized Vicsek model
• Conditional global entanglement in a Kosterlitz-Thouless quantum phase transition
• Ordering kinetics in q-state random-bond clock model: Role of Vortices and Interfaces
• Higher symmetry breaking and non-reciprocity in a driven-dissipative Dicke model