Unraveling critical dynamics: The formation and evolution of textures - art. no. 085002

We study the formation of texture topological defects in a nonequilibrium p hase transition of on overdamped classical O(3) model in 2 + 1 dimensions. The phase transition is triggered through an external, time-dependent effec tive mass, parametrized by the quench time scale tau. When measured near th e end of the transition ([<(Phi)over cap>(2)] = 0.9) the average texture se paration L-sep and the average texture width L-w scale as L-sep similar to tau(0.39+/-0.02) and L-w similar to tau(0.46+/-0.04), significantly larger than the single power-law xi(freeze) similar to tau(0.25) predicted from th e Kibble-Zurek mechanism. We show that Kibble-Zurek scaling is recovered at very early times but that by the end of the transition L-sep(tau) and L-w( tau) result instead from a competition between the length scale determined at freeze-out and the ordering dynamics of a textured system. We offer a si mple proposal for the dynamics of these length scales: L-sep(t) = xi(1)(tau ) + L-l(t - t(freeze)) and L-w(t) = xi(2)(tau) + L-2(t - t(freeze)) where x i(1) similar to tau(alpha) and xi(2) similar to tau(beta) are determined by the freeze-out mechanism, L-1(t) = (xi(1))(1/3)t(1/3) and L-2(t) = t(1/2) are dynamical Length scales previously known from phase ordering dynamics, and t(freeze) is the freeze-out time. We find that L-sep(t) and L-w(t) fit closely to the length scales observed at the end of the transition and yiel d alpha = 0.24+/-0.02 and beta = 0.22 +/- 0.07, in good agreement with the Kibble-Zurek mechanism. In the context of phase ordering these results sugg est that the multiple length scales characteristic of the late-time orderin g of a textured system derive from the critical dynamics of a single nonequ ilibrium correlation length. In the context of defect formation these resul ts imply that significant evolution of the defect network can occur before the end of the phase transition. Therefore a quantitative understanding of the defect network: at the end of the phase transition generally requires a n understanding of both critical dynamics and the interactions among topolo gical defects.