Phase transition temperatures at next-to-leading order.

Broken gauge symmetries are typically restored at high temperature, and the leadingorder result for the critical temperature Tc was found many years ago by Weinberg and by Dolan and Jackiw. I find a simple expression for the next-to-leading order correction to Tc, which is order eTc 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 λ is the same order as e, and it does not address the case of strongly first-order phase transitions, which arise when λ ≪ e.