O(N) linear sigma model beyond the Hartree approximation at finite temperature

TL;DR

This paper investigates the O(N) linear sigma model at finite temperature, extending the analysis beyond the Hartree approximation by including two-loop effects, revealing a second-order phase transition and analyzing temperature-dependent mass parameters.

Contribution

It introduces a two-loop correction to the 2PPI effective action in the sigma model, demonstrating a change from first to second-order phase transition compared to Hartree approximation.

Findings

Second-order phase transition identified with two-loop correction

Temperature dependence of variational mass parameters analyzed

Relation between variational masses and physical particle masses discussed

Abstract

We study the O(N) linear sigma model with spontaneous symmetry breaking at finite temperature in the framework of the two-particle point-irreducible (2PPI) effective action. We go beyond the Hartree approximation by including the two-loop contribution, i.e., the sunset diagram. A phase transition of second order is found, whereas it is of first order in the one-loop Hartree approximation. Furthermore, we show the temperature-dependence of the variational mass parameters and comment on their relation to the physical sigma and pion masses.