Thermal renormalization group equations and the phase transition of scalarO(N) theories - art. no. 105036

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 behavio r directly in terms of the zero-temperature physical couplings. They provid e a nonperturbative method for a computation of quantities such as real-tim e con elation 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 temperatur e, critical exponents and amplitudes as well as the scaling equation of sta te for self-interacting scalar theories. [S0556-2821(99)01720-8].