Thermal Mixing of Phases: Numerical and Analytical Studies

The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified assumptions concerning the complex mechanisms typical of nonequilibrium field theories. In particular, whenever first order phase transitions are invoked, the metastable background is assumed to be sufficiently smooth to justify the use of homogeneous nucleation theory in the computation of nucleation rates of critical bubbles. In this talk I present the results of numerical simulations which were designed to quantify ``smoothness''; that is, how the contribution from nonperturbative subcritical fluctuations may spoil the homogeneity assumption of nucleation theory. I then show how the numerical results can be understood {\it quantitatively} in terms of a simple analytical model of subcritical thermal fluctuations. Encouraged by the success of the model in matching the numerical results, I apply it to the standard model electroweak phase transition.