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

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.

4 pages, 3 figures