On phase ordering behind the propagating front of a second-order transition

In a real system the heating is nonuniform, and a second-order phase transition to a broken-symmetry phase occurs by propagation of a temperature front. Two parameters, the cooling rate τ Q and the transition front velocity ν T determine the nucleation of topological defects. Depending on the relation of these parameters, two regimes are found: in the regime of fast propagation defects are created according to the Zurek scenario for the homogeneous case, while in the slow-propagation regime vortex formation is suppressed.