---
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 $p>p_c$.'
author:
- 'Natascia Andrenacci$^\S$, Federico Corberi$^\dag$, and Eugenio Lippiello$^\ddag$'
title: 'Crossover between Ising and XY-like behavior in the off-equilibrium kinetics of the one-dimensional clock model'
---

§andrenacci@sa.infn.it

corberi@na.infn.it lippiello@sa.infn.it

PACS: 05.70.Ln, 75.40.Gb, 05.40.-a

Introduction {#intro}
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After quenching a ferromagnetic system to a low temperature phase, relaxation towards the new equilibrium state is realized by a progressive phase-ordering [@Bray94]. The specific mechanisms involved in the coarsening phenomenon depend on the presence and on the nature of 