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

Understand

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.