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

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.