Phase transition in the massive Gross-Neveu model in toroidal topologies

TL;DR

This paper investigates phase transitions in the massive Gross-Neveu model on toroidal topologies, revealing a confinement-deconfinement transition influenced by temperature and spatial compactification, with results comparable to hadronic scales.

Contribution

It introduces a quantum field theory analysis of the Gross-Neveu model on toroidal topologies, identifying phase transition points related to confinement and deconfinement.

Findings

Asymptotic freedom behavior observed as $g o 0$ when $L o 0$ or $T o abla$

Finite $L$ induces a phase transition to spatial confinement at strong coupling

Deconfining temperature and confining length are estimated for different dimensions

Abstract

We use methods of quantum field theory in toroidal topologies to study the $N$-component $D$-dimensional massive Gross-Neveu model, at zero and finite temperature, with compactified spatial coordinates. We discuss the behavior of the large-$N$ coupling constant ($g$), investigating its dependence on the compactification length ($L$) and the temperature ($T$). For all values of the fixed coupling constant ($\lambda$), we find an asymptotic-freedom type of behavior, with $g\to 0$ as $L\to 0$ and/or $T\to \infty$. At T=0, and for $\lambda \geq \lambda_{c}^{(D)}$ (the strong coupling regime), we show that, starting in the region of asymptotic freedom and increasing $L$, a divergence of $g$ appears at a finite value of $L$, signaling the existence of a phase transition with the system getting spatially confined. Such a spatial confinement is destroyed by raising the temperature. The confining length, $L_{c}^{(D)}$, and the deconfining temperature, $T_{d}^{(D)}$, are determined as functions of $\lambda$ and the mass ($m$) of the fermions, in the case of $D=2,3,4$. Taking $m$ as the constituent quark mass ($\approx 350\: MeV$), the results obtained are of the same order of magnitude as the diameter ($\approx 1.7 fm$) and the estimated deconfining temperature ($\approx 200\: MeV$) of hadrons.