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

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 $p>p_c$.

arXiv comment14 pages, 13 figures

References in corpus (6)

• Theory of Phase Ordering Kinetics
• Fluctuation dissipation ratio in the one dimensional kinetic Ising model
• Off-equilibrium generalization of the fluctuation dissipation theorem for Ising spins and measurement of the linear response function
• Coarsening in the q-State Potts Model and the Ising Model with Globally Conserved Magnetization
• Unwinding Scaling Violations in Phase Ordering
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Cited by in corpus (6)

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• Scaling in the Aging Dynamics of the Site-diluted Ising Model
• Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
• Phase ordering in disordered and inhomogeneous systems
• Phase ordering induced by defects in chaotic bistable media