FOAM DIAGRAM SUMMATION AT FINITE-TEMPERATURE

We show that large-N phi(4) theory is not trivial if one accepts the p resence of a tachyon with a truly huge mass, and that it allows exact calculation. We use it to illustrate how to calculate the exact resumm ed pressure at finite temperature and verify that it is infrared and u ltraviolet finite even in the zero-mass case. In three dimensions a re sidual effect of the resummed infrared divergences is that at low temp erature or strong coupling the leading term in the interaction pressur e becomes independent of the coupling and is 4/5 of the free-field pre ssure. In four dimensions the pressure is well defined provided that t he temperature is below the tachyon mass. We examine how rapidly this expansion converges and use our analysis to suggest how one might reor ganise perturbation theory to improve the calculation of the pressure for the QCD plasma. (C) 1998 Elsevier Science B.V.