THE ELECTROWEAK PHASE-TRANSITION THROUGH THE RENORMALIZATION-GROUP

We study the high-temperature phase transitions for the Abelian and SU (2) Higgs models, using the exact renormalization group, The evolution equation for a properly defined coarse-grained free energy is solved. The phase diagram of the Abelian Higgs model has a region of second-o rder phase transitions governed by fixed points, for which we calculat e critical exponents and crossover curves. It also has a region of fir st-order phase transitions, which we discuss in terms of the coarse-gr ained free energy. The SU(2) Higgs model for small Higgs field masses has only first-order phase transitions. We derive their properties and compare with lattice and perturbative results. For larger Higgs field masses the strength of the first-order phase transitions diminishes. For masses larger than 80-100 GeV we find evidence that they are repla ced by analytical crossovers.