# Critical end point in a thermo-magnetic nonlocal NJL model

## TL;DR

This paper investigates the phase diagram of a thermo-magnetic nonlocal NJL model, identifying how the critical end point shifts with magnetic field and chemical potential, revealing a critical magnetic field inducing a first order transition at zero chemical potential.

## Contribution

It introduces analysis of the critical end point in a nonlocal NJL model under magnetic fields, showing how the phase transition nature changes with magnetic field and chemical potential.

## Key findings

- Crossover at zero magnetic field becomes first order with increasing magnetic field.
- Critical end point shifts to higher temperature and lower chemical potential as magnetic field increases.
- Existence of a critical magnetic field causing a first order transition at zero chemical potential.

## Abstract

In this article we explore the critical end point in the $T-\mu$ phase diagram of a thermomagnetic nonlocal Nambu--Jona-Lasinio model in the weak field limit. We work with the Gaussian regulator, and find that a crossover takes place at $\mu, B=0$. The crossover turns to a first order phase transition as the chemical potential or the magnetic field increase. The critical end point of the phase diagram occurs at a higher temperature and lower chemical potential as the magnetic field increases. This result is in accordance to similar findings in other effective models. We also find there is a critical magnetic field, for which a first order phase transition takes place even at $\mu=0$.