Phase diagram of the large N Gross-Neveu model in a finite periodic box

R Narayanan

doi:10.1103/physrevd.101.096001

Abstract

We analyze the Gross-Neveu model in the limit of large number of flavors of massless fermions. We study the phase diagram in a two and three dimensional periodic box at a fixed thermal to spatial aspect ratio, $\frac{\beta}{\ell}$, with a flavor independent chemical potential. We assume the bilinear condensate, when one exists, has a specific momentum in the spatial direction(s). The main known features of the phase diagram in the $\ell\to\infty$ limit of the two dimensional model are also seen on a finite $\ell\times\beta$ torus -- a phase with a homogeneous (zero momentum) condensate; a phase with an inhomogeneous (non-zero momentum) condensate and a phase with no condensate. We observe that the inhomogeneous phase contains several sub-phases characterized by a specific spatial momentum. Unlike the two dimensional model, we do not find evidence for a phase with a inhomogeneous condensate in the three dimensional model.

Highlights

The two dimensional Gross-Neveu model [1] with N flavors of massless fermions and a flavor-singlet quartic self-interaction has been shown to be quite an interesting toy model with several features that mimic four dimensional QCD
We have studied the phase diagram of the Gross-Neveu model in the limit of large number of flavors in two and three dimensions
The presence or absence of a fermion bilinear condensate can be found by solving the gap equation and obtaining the global minimum of the effective action of the condensate

Summary

Introduction

The two dimensional Gross-Neveu model [1] with N flavors of massless fermions and a flavor-singlet quartic self-interaction has been shown to be quite an interesting toy model with several features that mimic four dimensional QCD. A complete Hartree-Fock calculation showed the presence of a phase with an inhomogeneous condensate [3]. This result was confirmed later using a lattice computation [4] that performed a brute force minimization of the free energy and studied instabilities. This model was numerically studied on the lattice at finite but large number of flavors (eight to be exact) [5] and was shown to have a phase with an inhomogeneous condensate

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Results

Conclusion