On the possibility of second-order phase transitions in spontaneously broken gauge theories

Abstract

In the “Type-II” regime, m Higgs ⪆ m gauge , the finite-temperature phase transition in spontaneously-broken gauge theories (including the standard model) must be studied using a renormalization group treatment. Previous studies within the (4- ϵ)-expansion suggest a 1st-order transition in this regime. We use analogies with experimentally accessible phase transitions in liquid crystals, and theoretical investigations of superconductor phase transitions to argue that, in this range, the critical behavior of a large class of gauge-Higgs-fermion systems changes from 1st-to 2nd-order as a function of Higgs mass. We identify a set of models which, within the (2+ ϵ)-expansion, possess fixed points that can describe this 2nd-order behavior. A definitive demonstration that the claimed critical behavior occurs (and a reliable estimate of m Higgs at the tricritical point) will probably require numerical simulations.