# Finite Size Analysis of the U(1) Background Field Effective Action

## TL;DR

This paper uses finite size scaling to analyze the effective action derivative in lattice U(1) gauge theory under a magnetic field, identifying a continuous phase transition and estimating critical parameters consistent with specific heat analysis.

## Contribution

It introduces a finite size scaling approach to study the effective action in lattice U(1) gauge theory, revealing a continuous phase transition and providing critical parameter estimates.

## Key findings

- Identified a continuous phase transition in the model.
- Estimated critical parameters consistent with specific heat analysis.
- Validated finite size scaling as an effective method for this system.

## Abstract

We apply the finite size scaling analysis to the derivative of the density of the effective action for the lattice U(1) pure gauge theory in an external constant magnetic field. We found the presence of a continuous phase transition. Moreover, our extimate of of the critical parameters gives values consistent with those extracted from the analysis of the specific heat.