  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.
