Resummation of soft modes in the free energy of Phi^4 theory

Abstract

A new method is proposed for the calculation of the free energy of an N-component Phi^4 theory at finite temperature. The method combines a perturbative treatment of the hard modes with a non-perturbative treatment in the effectively three-dimensional sector of the soft modes. The separation between hard and soft modes is achieved by the effective field theory method of Braaten and Nieto. One- and two-loop gap equations for the screening mass are used to resum higher order effects in the soft sector. The proposed method is similar to the screened perturbation theory of Karsch, Patkos, and Petreczky albeit avoiding the difficulty of solving gap equations in the full four-dimensional theory. Since gap equations are only used in the three-dimensional effective theory the tedious evaluation of Matsubara sums is not necessary. This simplification makes it possible to go beyond the one-loop gap equation. The large N as well as the finite N case are discussed.