Finite-size effects on the phase structure of the Nambu-Jona-Lasinio model

TL;DR

This paper studies how finite-size effects influence the phase structure of the NJL model in three dimensions, using zeta-function and compactification methods to analyze phase transitions at various sizes and temperatures.

Contribution

It provides a detailed analysis of finite-size effects on the NJL model's phase structure in three dimensions, including critical lines and phase transitions, using advanced mathematical techniques.

Findings

Finite-size effects modify the phase boundaries.

Critical lines for phase transitions are derived.

Finite temperature effects are incorporated as a compactified dimension.

Abstract

The Nambu-Jona-Lasinio (NJL) model is one of the most frequently used four-fermion models in the study of dynamical symmetry breaking. In particular, the NJL model is convenient for that analysis at finite temperature, chemical potential and size effects, as has been explored in the last decade. With this motivation, we investigate the finite-size effects on the phase structure of the NJL model in $D = 3$ Euclidean dimensions, in the situations that one, two and three dimensions are compactified. In this context, we employ the zeta-function and compactification methods to calculate the effective potential and gap equation. The critical lines that separate trivial and non-trivial fermion mass phases in a second order transition are obtained. We also analyze the system at finite temperature, considering the inverse of temperature as the size of one of the compactified dimensions.