Variational Study of the Phase Transition at Finite T in the $\lambda \phi^4 $-Theory

TL;DR

This paper investigates the phase transition in the 4D $bbbphi^4$-theory using a self-consistent method, revealing a second order transition at zero temperature and a weakly first order transition at finite temperature, consistent with triviality.

Contribution

It applies a Feynman-Bogoliubov self-consistent approach to analyze the phase transition, providing insights into the nature of the transition at finite temperature.

Findings

Second order phase transition at zero temperature.

Transition becomes weakly first order at finite temperature.

Renormalized coupling constant approaches zero as cutoff is removed.

Abstract

Assuming triviality of the 4-dimensional $\lambda \phi ^4$-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 $\Lambda $ is removed the renormalized self coupling constant $\lambda _R$ goes to zero consistent with the claim of triviality. At finite temperature the phase transition becomes weakly first order.