We investigate the dynamics of second-order phase transitions in two dimensions, breaking a gauged U(1) symmetry. Using numerical simulations, we show that the density of the topological defects formed scales with the quench time scale τQ as n~τQ^-1/2 when the dynamics is overdamped at the instant when the freeze-out of thermal fluctuations takes place, and n~τQ^-2/3 in the underdamped case. This is predicted by the scenario proposed by one of us (W. H. Z.).
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Yates et al. (1998) studied this question.
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