2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/198636We report the first large scale numerical study of the dynamics of the second order phase transition of a U(1) $λϕ^4$ theory in three spatial dimensions. The transition is induced by a time-dependent temperature drop in the heat bath to which the fields are coupled. We present a detailed account of the dynamics of the fields and vortex string formation as a function of the quench rate. The results are found in good agreement to the theory of defect formation proposed by Kibble and Zurek.4 pages, 4 figures, RevTexHigh Energy Physics - Phenomenologytext