The Thermodynamic Bethe Ansatz and the 1/N Correction to the Density Phase Transition in the Gross-Neveu Model

TL;DR

This paper calculates the first-order correction in 1/N to the critical chemical potential at which a phase transition occurs in the Gross-Neveu model, using thermodynamic Bethe ansatz and effective potential methods.

Contribution

It provides the first 1/N correction to the phase transition point in the Gross-Neveu model employing thermodynamic Bethe ansatz techniques.

Findings

The corrected critical chemical potential is rac{m}{\u221a{2}}[1 - rac{0.47}{N}]

The correction accounts for finite N effects on the phase transition

The approach combines free energy from Bethe ansatz with zero chemical potential effective potential.

Abstract

We compute the $1/N$ correction to the location of the previously found first-order phase transition in the Gross-Neveu model at a chemical potential $\mu = \mu_c = {1 \over \sqrt{2}} m$, where $m$ is the fermion mass. We employ an expression for the free energy $f(\mu)$ given by the thermodynamic Bethe ansatz under the approximation that the fundamental fermions dominate the ground state, and combine it with the effective potential evaluated at zero chemical potential. Our result is $\mu_c = {m \over \sqrt{2}} [1 - {0.47 \over N}]$.