# Finite-volume and magnetic effects on the phase structure of the three-flavor Nambu--Jona-Lasinio model

## TL;DR

This paper investigates how finite volume and magnetic fields influence the phase structure of a three-flavor Nambu--Jona-Lasinio model, revealing effects on chiral symmetry breaking and phase transitions under various conditions.

## Contribution

It introduces a detailed analysis of finite-volume and magnetic effects on the NJL model with three quark flavors using mean-field and Schwinger methods, including 't Hooft interactions.

## Key findings

- Reducing volume favors chiral symmetry restoration.
- Magnetic fields enhance chiral symmetry breaking.
- Phase transition characteristics depend on temperature, chemical potential, and magnetic field.

## Abstract

In this work we analyze the finite-volume and magnetic effects on the phase structure of a generalized version of Nambu--Jona-Lasinio model with three quark flavors. By making use of mean-field approximation and Schwinger's proper-time method in a toroidal topology with antiperiodic conditions, we investigate the gap equation solutions under the change of the size of compactified coordinates, strength of magnetic field, temperature and chemical potential. The 't Hooft interaction contributions are also evaluated. The thermodynamic behavior is strongly affected by the combined effects of relevant variables. The findings suggest that the broken phase is disfavored due to both increasing of temperature and chemical potential, and the drop of the cubic volume of size $L$, whereas it is stimulated with the augmentation of magnetic field. In particular, the reduction of $L$ (remarkably at $L\approx 0.5 - 3 $~fm) engenders a reduction of the constituent masses for $u,d,s$-quarks through a crossover phase transition to the their corresponding current quark masses. On the other hand, the presence of a magnetic background generates greater values constituent quark masses, inducing smaller sizes and greater temperatures at which the constituent quark masses drop to the respective current ones.