Abstract
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 ${\ensuremath{\tau}}_{Q}$ as $n\ensuremath{\sim}{\ensuremath{\tau}}_{Q}^{\ensuremath{-}1/2}$ when the dynamics is overdamped at the instant when the freeze-out of thermal fluctuations takes place, and $n\ensuremath{\sim}{\ensuremath{\tau}}_{Q}^{\ensuremath{-}2/3}$ in the underdamped case. This is predicted by the scenario proposed by one of us (W. H. Z.).
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