# Critical behaviour of an effective relativistic mean field model in the presence of magnetic background and boundaries

## TL;DR

This study explores how magnetic fields and boundary conditions influence the thermodynamic behavior of relativistic mean field models, revealing complex phase structures and effects on long-range correlations.

## Contribution

It introduces a combined analysis of magnetic background and boundary effects on relativistic mean field models using a generalized zeta-function approach.

## Key findings

- Long-range correlations are significantly affected by magnetic field and boundary size.
- Symmetric phase is favored due to inverse magnetic catalysis and reduced compactification.
- Rich phase structure emerges from the parameter space exploration.

## Abstract

In the present work we investigate the combined influence of magnetic background and boundaries on the thermodynamic properties of effective relativistic mean field models, like the so-called Walecka model. This is done by making use of generalized zeta-function approach and mean-field approximation at effective chemical equilibrium, focusing on the dependence with the size of compactified spatial dimension, the temperature and the magnetic field strength. The findings suggest a rich phase structure in the parameter space. The maintenance of long-range correlations is strongly affected under the change of these parameters, with the symmetric phase being favoured due to both inverse magnetic catalysis effect and the reduction of size of compactified dimension.