Thermal renormalization group equations and the phase transition of scalar O(N) theories

We discuss the formulation of “thermal renormalization group equations” and their application to the finite temperature phase transition of scalar O(N) theories. Thermal renormalization group equations allow for a computation of both the universal and the nonuniversal aspects of the critical behavior directly in terms of the zero-temperature physical couplings. They provide a nonperturbative method for a computation of quantities such as real-time correlation functions in a thermal environment, where in many situations straightforward perturbation theory fails due to the bad infrared behavior of the thermal fluctuations. We present results for the critical temperature, critical exponents and amplitudes as well as the scaling equation of state for self-interacting scalar theories.