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We revisit the Kibble-Zurek mechanism by analyzing the dynamics of phaseordering systems during an infinitely slow annealing across a second orderphase transition. We elucidate the time and cooling rate dependence of thetypical growing length and we use it to predict the number of topologicaldefects left over in the symmetry broken phase as a function of time, bothclose and far from the critical region. Our results extend the Kibble-Zurekmechanism and reveal its limitations.

Kibble-Zurek mechanism and infinitely slow annealing through critical points