# A Model to Study Finite-Size and Magnetic Effects on the Phase Transition of a Fermion Interacting System

## TL;DR

This paper introduces a model to analyze how finite size, magnetic fields, and chemical potential influence phase transitions in a fermionic system with four- and six-fermion interactions, revealing complex phenomena like magnetic catalysis and inverse symmetry breaking.

## Contribution

The study generalizes the Matsubara method to include finite size and magnetic effects, providing new insights into phase transition behavior in interacting fermionic systems.

## Key findings

- Strong dependence of transition temperature on coupling constants
- Observation of magnetic catalysis and symmetry breaking
- Discovery of inverse symmetry breaking in first-order transitions

## Abstract

We present a model to study effects from an external magnetic field, chemical potential, and finite size, on the phase structure of a massive four- and six-fermion interacting system. These effects are introduced by a method of compactification of coordinates, a generalization of the standard Matsubara prescription. Through the compactification of the $z$ coordinate and of imaginary time, we describe a heated system with the shape of a film of thickness $L$, at temperature $\beta^{-1}$ undergoing first- or second-order phase transition. We have found a strong dependence of the temperature transition on the constants couplings $\lambda$ and $\eta$. Besides magnetic catalysis and symmetry breaking for both kinds of transition, we have found an inverse symmetry breaking phenomenon with respect to first-order phase transition.