Radiatively-Induced First-Order Phase Transitions: The Necessity of the Renormalization Group

Details Radiatively-Induced First-Order Phase Transitions: The Necessity of the Renormalization Group Radiatively-Induced First-Order Phase Transitions: The Necessity of the Renormalization Group

1993-08-31

arxiv.org/abs/hep-ph/9308364v2

Nucl.Phys. B417 (1994) 527-552

Physics

High Energy Physics

High Energy Physics - Phenomenology

26 pages, two figures, LaTex macropackage. References added and appendix A revised. LBL preprint LBL-34573

Scientific paper

10.1016/0550-3213(94)90483-9

We advocate a (Wilson) renormalization-group (RG) treatment of finite-temperature first-order phase transitions, in particular those driven by radiative corrections such as occur in the standard model, and other spontaneously-broken gauge theories. We introduce the scale-dependent coarse-grained free energy $S_\La[\phi]$ which we explicitly calculate, using the Wilson RG and a $(4-\ep)$-expansion, for a scalar toy model that shares many features of the gauged case. As argued by Langer and others, the dynamics of the phase transition are described by $S_\La[\phi]$ with $\La$ of order the bubble wall thickness, and {\it not} by the usual (RG-improved) finite-temperature effective action which is reproduced by $S_\La[\phi]$ for $\La\to 0$. We argue that for weakly first-order transitions (such as that in the standard model) the $(4-\ep)$-expansion is necessary to control an inevitable growth of the effective scale-dependent coupling towards the strong-coupling regime, and that diagrammatic resummation techniques are unlikely to be appropriate.

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