On the Infrared Behavior of the Pressure in Thermal Field Theories

We study non-perturbatively, via the Schwinger-Dyson equations, the leading infrared behavior of the pressure in the ladder approximation. This problem is discussed firstly in the context of a thermal scalar field theory, and the analysis is then extended to the Yang-Mills theory at high temperatures. Using the Feynman gauge, we find a system of two coupled integral equations for the gluon and ghost self-energies, which is solved analytically. The solutions of these equations show that the contributions to the pressure, when calculated in the ladder approximation, are finite in the infrared domain.