Cooper pairing and finite-size effects in a NJL-type four-fermion model

TL;DR

This paper investigates how finite-size effects and boundary conditions influence phase transitions, condensates, and particle densities in a NJL-type four-fermion model at nonzero chemical potential and zero temperature.

Contribution

It analyzes the impact of space topology and boundary conditions on phase structures and critical phenomena in a NJL model, revealing oscillatory behavior and shifts in phase transition points.

Findings

Critical curves oscillate with boundary length L.

Superconducting phase transition shifts to smaller μ at finite L.

Condensates and densities strongly depend on boundary conditions.

Abstract

Starting from a NJL-type model with N fermion species fermion and difermion condensates and their associated phase structures are considered at nonzero chemical potential $\mu$ and zero temperature in spaces with nontrivial topology of the form $S^1\otimes S^1\otimes S^1$ and $R^2\otimes S^1$. Special attention is devoted to the generation of the superconducting phase. In particular, for the cases of antiperiodic and periodic boundary conditions we have found that the critical curve of the phase transitions between the chiral symmetry breaking and superconducting phases as well as the corresponding condensates and particle densities strongly oscillate vs $\lambda\sim 1/L$, where $L$ is the length of the circumference $S^1$. Moreover, it is shown that at some finite values of $L$ the superconducting phase transition is shifted to smaller values both of $\mu$ and particle density in comparison with the case of $L=\infty$.