Crossover between Ising and XY-like behavior in the off-equilibrium kinetics of the one-dimensional clock model

TL;DR

This paper investigates the off-equilibrium dynamics of the one-dimensional p-state clock model, revealing a critical point at p=4 where the behavior transitions from Ising-like to XY-like, with a crossover observed at finite temperatures.

Contribution

It identifies a critical p-value in the clock model where the dynamical behavior shifts from Ising to XY-like, and characterizes the crossover during phase ordering.

Findings

For p ≤ 4, dynamics resemble the Ising model with interface annihilation.

For p > 4, dynamics are dominated by XY-like textures and scaling violations.

At finite temperature, a crossover from XY-like to Ising-like behavior occurs during phase ordering.

Abstract

We study the phase-ordering kinetics following a quench to a final temperature $T_f$ of the one-dimensional p-state clock model. We show the existence of a critical value $p_c=4$, where the properties of the dynamics change. At $T_f=0$, for $p\le p_c$ the dynamics is analogous to that of the kinetic Ising model, characterized by Brownian motion and annihilation of interfaces. Dynamical scaling is obeyed with the same dynamical exponents and scaling functions of the Ising model. For $p>p_c$, instead, the dynamics is dominated by a texture mechanism analogous to the one-dimensional XY model, and dynamical scaling is violated. During the phase-ordering process at $T_f>0$, before equilibration occurs, a cross-over between an early XY-like regime and a late Ising-like dynamics is observed for $p>p_c$.