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We study the full out-of-thermal-equilibrium dynamics of a relativisticclassical scalar field through a symmetry breaking phase transition. In thesecircumstances we determine the evolution of the ensemble averages of thecorrelation length and topological defect densities. This clarifies manyaspects of the non-perturbative dynamics of fields in symmetry breaking phasetransitions and allows us to comment on a quantitative basis on the canonicalpictures for topological defect formation and evolution. We also compare theseresults to those obtained from the field evolution in the Hartree approximationor using the linearized theory. By doing so we conclude about the regimes ofvalidity of these approximations.

Out of equilibrium dynamics of quench-induced spontaneous symmetry breaking and topological defect formation