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

Source: [Crossover between Ising and XY-like behavior in the off-equilibrium kinetics of the one-dimensional clock model](<https://www.sota2.com/research/paper/68fa27632c2a3760193c2557>)

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

Data updated: 2025-10-24T11:56:53.751Z

Authors: Natascia Andrenacci, Federico Corberi, Eugenio Lippiello

Published: 2006-09-13T14:17:35.000Z

## 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 $p\>p\_c$.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0609320>)

[PDF](<https://arxiv.org/pdf/cond-mat/0609320.pdf>)