Finite-size effects on the chiral phase diagram of four-fermion models in four dimensions

TL;DR

This paper investigates how finite size and boundary conditions in four-dimensional four-fermion models influence chiral symmetry breaking, revealing critical sizes and phase transition behaviors affected by temperature and chemical potential.

Contribution

It provides a detailed analysis of finite-size effects on the chiral phase diagram, including the existence of a critical compactification length and the impact on phase transition order.

Findings

Boundaries reduce the chiral breaking region.

A critical size exists below which symmetry breaking is suppressed.

Finite temperature and chemical potential alter the phase structure and transition order.

Abstract

We study the size dependence of the dynamical symmetry breaking in the four-dimensional Nambu-Jona-Lasinio model. We show that the presence of boundaries reduces the chiral breaking region, and this effect is strengthened for a larger number of compactified dimensions. A critical value for the length of the compactified dimensions exists, below which the dynamical symmetry breaking is not possible. Considering finite temperature and chemical potential, the chiral phase structure for the system with compactified dimensions is obtained. A gradual decreasing of the chiral breaking region with increasing of chemical potential is found. Also, at fixed chemical potential, the decreasing of the size of the system changes the order of the chiral phase transition.