Renormalisation of the non-perturbative thermal pressure

We show how the fully resummed thermal pressure is rendered ultraviolet finite by standard zero-temperature renormalisation. The analysis is developed in a six-dimensional scalar model that mimics QED and has N flavours. The N --> infinity limit of the model can be calculated completely. At a critical temperature, one of the degrees of freedom has vanishing screening mass like the transverse gauge bosons in four-dimensional finite-temperature perturbation theory, The renormalised non-perturbative interaction pressure of this model is evaluated numerically. (C) 1999 Elsevier Science B.V.