PERFECT 3-DIMENSIONAL LATTICE ACTIONS FOR 4-DIMENSIONAL QUANTUM-FIELDTHEORIES AT FINITE-TEMPERATURE

We propose a two-step procedure to study the order of phase transition s at finite temperature in electroweak theory and in simplified models thereof. In a first step a coarse grained free energy is computed by perturbative methods. It is obtained in the form of a 3-dimensional pe rfect lattice action by a block spin transformation. It has finite tem perature-dependent coefficients, In this way the UV-problem and the in frared problem are separated in a clean way, In the second step the ef fective 3-dimensional lattice theory is treated in a nonperturbative w ay, either by the Feynman-Bogoliubov method (solution of a gap equatio n), by real space renormalization group methods, or by computer simula tions. In this paper we outline the principles for phi(4)-theory and s calar electrodynamics. The Balaban-Jaffe block spin transformation for the gauge field is used. It is known how to extend this transformatio n to the nonabelian case, but this will not be discussed here.