Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1996-08-08
Nucl.Phys. B488 (1997) 92-140
Physics
High Energy Physics
High Energy Physics - Phenomenology
48 pages, 17 figures (some additions to the labels included in the captions), LaTeX file
Scientific paper
10.1016/S0550-3213(97)00037-0
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-order phase transitions governed by fixed points, for which we calculate critical exponents and crossover curves. It also has a region of first-order phase transitions, which we discuss in terms of the coarse-grained 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 replaced by analytical crossovers.
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