PHASE-TRANSITION TEMPERATURES AT NEXT-TO-LEADING ORDER

Broken gauge symmetries are typically restored at high temperature, and the leading-order result for the critical temperature T(c), has been known for many years. I find a simple expression for the next-to-leading-order correction to T(c), which is order eT(c) where e is the gauge coupling. The result is a simple consequence of recent work on summing ring diagrams at high temperature in gauge theories. The result is valid when the Higgs self-coupling-lambda is the same order as e2, and it does not address the case of strongly first-order phase transitions, which arise when lambda much less than e2.