Breakdown of Scaling in the Nonequilibrium Critical Dynamics of the Two-Dimensional XY Model

TL;DR

This paper investigates how the nonequilibrium critical dynamics of the 2D XY model depend on initial conditions, revealing a breakdown of the usual single scaling length and showing different growth laws for vortex-free and vortex-present initial states.

Contribution

It demonstrates that the approach to equilibrium in the 2D XY model exhibits different scaling behaviors depending on initial vortex presence, challenging the standard single-length scaling theory.

Findings

Growth law $\xi(t) o t^{1/2}$ without vortices

Growth law $\xi(t) o (t/\ln t)^{1/2}$ with vortices

Initial conditions critically affect nonequilibrium scaling

Abstract

The approach to equilibrium, from a nonequilibrium initial state, in a system at its critical point is usually described by a scaling theory with a single growing length scale, $\xi(t) \sim t^{1/z}$, where z is the dynamic exponent that governs the equilibrium dynamics. We show that, for the 2D XY model, the rate of approach to equilibrium depends on the initial condition. In particular, $\xi(t) \sim t^{1/2}$ if no free vortices are present in the initial state, while $\xi(t) \sim (t/\ln t)^{1/2}$ if free vortices are present.