Finite temperature phase transitions in quantum field theory

Abstract

Using the formalism developed previously the authors discuss finite temperature quantum field theory in the high temperature regime T>>mT where mT represents a generic finite temperature mass in the theory. In particular they consider lambda phi 4 theory in four dimensions showing perturbatively that it has a nontrivial fixed point at finite temperature, the relevant anomalous dimensions near the second-order phase transition being three-dimensional ones. They emphasize the importance of having renormalization schemes and a renormalization group (RG) equation that can explicitly take into account the fact that the degrees of freedom of a theory may be qualitatively different at different scales.