Domain Formation in Finite-Time Quenches

We study the formation of domains in a continuous phase transition with a finite-temperature quench. The model treated is the ${\mathrm{\Phi }}^4$ theory in two spatial dimensions with global O(2) symmetry. We investigate this using real-time thermal field theory, following Boyanovsky and collaborators, and find that domain sizes appear to be smaller than those produced in an instantaneous quench in the tree-level approximation. We also propose that a more physical picture emerges by examining the two-point functions which do not involve any cutoff on the short wavelength Goldstone modes.