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

Source: [Ordering kinetics in q-state clock model: scaling properties and growth laws](<https://www.sota2.com/research/paper/68fa3cad1e209131ce8dc7e2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T01:16:02.753Z

Authors: Swarnajit Chatterjee, Sanjay Puri, Raja Paul

Published: 2018-11-20T08:35:18.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1811.08121>)

[PDF](<https://arxiv.org/pdf/1811.08121.pdf>)