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

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

2006-09-13

arxiv.org/abs/cond-mat/0609320v1

Phys. Rev. E 74 (2006)

Physics

Condensed Matter

Statistical Mechanics

14 pages, 13 figures

Scientific paper

10.1103/PhysRevE.74.031111

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 $p>p_c$.

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