CRITICAL PHENOMENA IN-FIELD THEORIES AT FINITE-TEMPERATURE

It is shown how renormalization-group techniques which have been succe ssfully applied to critical phenomena in condensed-matter systems can be adapted to the study of phase transitions in field theories at fini te temperature. Explicit calculations are described for the simplest c ase of a self-interacting scalar field. A systematic method of estimat ing the transition temperature to all orders of renormalized perturbat ion theory is given, and the two-loop contribution is found. It appear s, however, that there is an additional, non-perturbative contribution which is not determined in the present work. An improved approximatio n to the effective potential is obtained, in which the renormalization group is used to resum the infrared singularities of perturbation the ory. This shows that the transition is of second order. disproving rec ent claims to the contrary. Gauge theories are discussed qualitatively , While application of the techniques described in this paper will pro bably show that the transitions in some gauge theories are of first or der, it is argued that the order of these transitions can probably not be detetermined reliably using methods currently available.