On the finite temperature $\lambda\varphi^{4}$ and Gross-Neveu models. Is there a first order phase transition in $(\lambda\varphi^{4})_{D=3}$?

TL;DR

This paper investigates finite temperature effects in the $ ext{}\lambda ext{ }\varphi^{4}$ and Gross-Neveu models, revealing a possible first order phase transition in the three-dimensional $ ext{(}\lambda ext{ }\varphi^{4} ext{)}_{D=3}$ model and analyzing thermal corrections.

Contribution

It provides a detailed analysis of thermal behavior in these models, highlighting the conditions for phase transitions and the temperature dependence of coupling constants.

Findings

Thermal mass increases with temperature in the $ ext{ }\lambda ext{ }\varphi^{4}$ model.

Thermal coupling constant decreases with temperature in the $ ext{ }\lambda ext{ }\varphi^{4}$ model.

A first order phase transition is possible in the $( ext{ }\lambda ext{ }\varphi^{4})_{D=3}$ model above a critical temperature.

Abstract

We study the behavior of two diferent models at finite temperature in a $D$-dimensional spacetime. The first one is the $\lambda\varphi^{4}$ model and the second one is the Gross-Neveu model. Using the one-loop approximation we show that in the $\lambda\varphi^{4}$ model the thermal mass increase with the temperature while the thermal coupling constant decrese with the temperature. Using this facts we establish that in the $(\lambda\varphi^{4})_{D=3}$ model there is a temperature $\beta^{-1}_{\star}$ above which the system can develop a first order phase transition, where the origin corresponds to a metastable vacuum. In the massless Gross-Neveu model, we demonstrate that for $D=3$ the thermal correction to the coupling constant is zero. For $D\neq 3$ our results are inconclusive. Pacs numbers: 11.10.Ef, 11.10.Gh