Three Dimensional Gross-Neveu Model on Curved Spaces

TL;DR

This paper investigates the critical behavior of the large N 3D Gross-Neveu model on curved spaces with constant curvature, analyzing phase properties and thermodynamics using zeta-function regularization.

Contribution

It extends the study of the Gross-Neveu model to curved manifolds, providing new insights into its critical properties and phase transitions on such geometries.

Findings

Evaluation of free energy density on curved spaces

Analysis of spontaneous magnetization and correlation length

Behavior of the model in zero temperature limit

Abstract

The large N limit of the 3-d Gross-Neveu model is here studied on manifolds with positive and negative constant curvature. Using the $\zeta$-function regularization we analyze the critical properties of this model on the spaces $S^2 \times S^1$ and $H^2\times S^1$. We evaluate the free energy density, the spontaneous magnetization and the correlation length at the ultraviolet fixed point. The limit $S^1\to R$, which is interpreted as the zero temperature limit, is also studied.