Temperature phase transition and an effective expansion parameter in the O(N)-model

TL;DR

This paper investigates the temperature-induced phase transition in the N-component scalar field theory, revealing it is weakly first order and becomes second order as N approaches infinity, using perturbative resummation techniques.

Contribution

It introduces a detailed perturbative analysis with resummations beyond the super daisy level, clarifying the nature of the phase transition in the O(N)-model.

Findings

Phase transition is weakly first order at finite N.

Transition becomes second order as N approaches infinity.

Higher-order diagrams do not qualitatively change the transition.

Abstract

The temperature phase transition in the N-component scalar field theory with spontaneous symmetry breaking is investigated in the perturbative approach. The second Legendre transform is used together with the consideration of the gap equations in the extrema of the free energy. Resummations are performed on the super daisy level and beyond. The phase transition turns out to be weakly of first order. The diagrams beyond the super daisy ones which are calculated correspond to next-to-next-to-leading order in 1/N. It is shown that these diagrams do not alter the phase transition qualitatively. In the limit N goes to infinity the phase transition becomes second order. A comparison with other approaches is done.