Scaling and universality in the aging kinetics of the two-dimensional clock model

TL;DR

This study investigates the aging dynamics of the two-dimensional p-state clock model, revealing universal scaling behavior similar to non-disordered coarsening systems and establishing its relation to the Ising universality class.

Contribution

It provides the first detailed numerical analysis of aging kinetics in the 2D clock model, demonstrating its universality class and scaling properties.

Findings

The model exhibits scaling behavior characteristic of non-disordered coarsening systems.

The dynamical exponents suggest the model belongs to the Ising universality class.

The integrated response function follows a specific scaling form with an exponent consistent with the 2D Ising model.

Abstract

We study numerically the aging dynamics of the two-dimensional p-state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior characteristic of non-disordered coarsening systems. For quenches to the ferromagnetic phase, the value of the dynamical exponents, suggests that the model belongs to the Ising-type universality class. Specifically, for the integrated response function $\chi (t,s)\simeq s^{-a_\chi}f(t/s)$, we find $a_\chi $ consistent with the value $a_\chi =0.28$ found in the two-dimensional Ising model.