# Influence of external magnetic field, finite-size effects and chemical potential on the phase transition of a complex scalar field

## TL;DR

This paper investigates how external magnetic fields, finite-size effects, and chemical potential influence the phase transition of a complex scalar field, providing insights into critical behavior in constrained quantum systems.

## Contribution

The study introduces a scalar quantum field model on toroidal topologies to analyze phase transitions under combined external magnetic and finite-size effects, comparing results with Ginzburg-Landau theory.

## Key findings

- Critical temperature depends on magnetic field strength and film thickness.
- Finite-size effects shift the phase transition point.
- The model aligns with second-order phase transition characteristics and Ginzburg-Landau predictions.

## Abstract

A scalar model is built, as a quantum field theory defined on toroidal topologies, to describe phase transition in films subjected to periodic boundary conditions and influenced by an external and constant magnetic field. Criticality is studied and the relations between the critical temperature, the film thickness, the magnetic field strength and the chemical potential are investigated. Since the model describes a second-order phase transition a comparison with the Ginzburg-Landau theory is made.