Variational Study of the Phase Transition at Finite T in the $λϕ^4 $-Theory

Abstract

Assuming triviality of the 4-dimensional $λϕ^4$-theory we compute the effective potential by means of a self consistent Feynman-Bogoliubov method. This potential $U_{eff}^{FB}$ 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 $Λ$ is removed the renormalized self coupling constant $λ_R$ goes to zero consistent with the claim of triviality. At finite temperature the phase transition becomes weakly first order.