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
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
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
