Abstract

Assuming triviality of the 4-dimensional ?? 4-theory we compute the effective potential by means of a self consistent Feynman-Bogoliubov method. This potential U FB eff depends on a UV-cutoff, which is fixed by a stability condition for the gap-equation for the plasma mass. 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 ? is removed the renormalized self coupling constant \R goes to zero consistent with the claim of triviality. At finite temperature the phase transition becomes weakly first order.