# The gauged Nambu - Jona Lasinio model: a mean field calculation with non mean field exponents

## TL;DR

This paper investigates the phase diagram of the lattice gauged Nambu-Jona Lasinio model using mean field theory and numerical simulations, revealing a phase transition line and suggesting non-mean-field critical exponents.

## Contribution

It combines mean field approximation with numerical simulations to analyze the phase structure and critical behavior of the gauged Nambu-Jona Lasinio model.

## Key findings

- Identifies a phase transition line separating broken and symmetric phases.
- Mean field exponents relate to the chiral condensate in Coulomb phase.
- Numerical results suggest non-mean-field critical exponents.

## Abstract

We analyse the phase diagram of the lattice gauged Nambu-Jona Lasinio model with the help of a mean field approximation plus numerical simulations. We find a phase transition line in the coupling parameters space separating the chirally broken phase from the symmetric phase, which is in good qualitative agreement with results obtained in the quenched-ladder approximation. The mean field approximation relates the critical exponents along the continuous phase transition line with the mass dependence of the chiral condensate in the Coulomb phase of standard noncompact $QED$. Our numerical results for noncompact $QED$ strongly suggest non mean field exponents along the critical line.