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We report the first large scale numerical study of the dynamics of a second order phase transition caused by a gradual decrease of temperature in a U (1) ^4 theory in three spatial dimensions. We present a detailed account of the dynamics of the fields and focus on vortex string formation as a function of the quench rate. The results are found in good agreement with the theory of defect formation proposed by Kibble and Zurek.
Antunes et al. (1999) studied this question.