Vortex String Formation in a 3D U(1) Temperature Quench

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) $\lambda {\phi }^4$ 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.