Second and first order phase transition in three dimension Gross-Neveu model

TL;DR

This paper analyzes phase transitions in the three-dimensional Gross-Neveu model, revealing second order transitions at finite temperature and first order at zero temperature with finite chemical potential, identifying a tricritical point.

Contribution

It provides a detailed critical analysis of the order of phase transitions in the model, including the identification of a tricritical point and verification via effective potential methods.

Findings

Second order phase transition at finite T

First order phase transition at T=0 with finite μ

Identification of a tricritical point at (T, μ) = (0, m(0))

Abstract

Symmetry restoring phase transitions in three dimension Gross-Neveu model are shown to be second order at finite temperature $T$ and first order at T=0 and finite chemical potential $\mu$ by critical analysis of the dynamical fermion mass based on the gap equation. The latter is further verified by effective potential analysis. The resulting tricritical point is $(T,\mu)=(0,m(0))$, where $m(0)$ is the dynamical fermion mass at $T=\mu=0$. Physical difference between the above second and first order phase transition is illustrated by means of variations of thermodynamical particle density.