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 syst em at its critical point is usually described by a scaling theory with a si ngle growing length scale, xi(t) similar to 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 conditio n. In particular, xi(t) similar to t(1/2) if no free vortices are present i n the initial state, while xi(t) similar to (t/lnt)(1/2) if free vortices a re present.