VARIATIONAL STUDY OF THE PHASE-TRANSITION AT FINITE-T IN THE LAMBDA-PHI(4)-THEORY

Assuming triviality of the 4-dimensional lambda phi(4)-theory we compu te the effective potential by means of a self consistent Feynman-Bogol iubov method. This potential U-eff(FB) depends on a UV-cutoff, which i s fixed by a stability condition for the gap-equation for the plasma m ass. It shows a second order phase transition at zero temperature, in agreement with a large amount of analytical and RG analysis as well as Monte Carlo numerical evidence. As the cutoff Lambda is removed the r enormalized self coupling constant lambda(R) goes to zero consistent w ith the claim of triviality. At finite temperature the phase transitio n becomes weakly first order.