# Order parameters and boundary effects in U(1) lattice gauge theory

## TL;DR

This paper introduces a new order parameter based on boundary effects and current networks to distinguish phases in 4D U(1) lattice gauge theory, providing an efficient way to identify phase transitions.

## Contribution

It demonstrates that the probability of an 'infinite' current network serves as a boundary-condition-independent order parameter for phase characterization.

## Key findings

- Probability of 'infinite' network is 0 in cold phase and 1 in hot phase.
- The order parameter effectively identifies the transition region.
- Boundary inhomogeneities can lead to the reappearance of an energy gap.

## Abstract

We show that, independently of the boundary conditions, the two phases of the 4-dimensional compact U(1) lattice gauge theory can be characterized by the presence or absence of an ``infinite'' current network, with an appropriate definition of ``infinite'' for the various types of boundary conditions imposed on the finite lattice. The probability for the occurrence of an ``infinite'' network takes values 0 or 1 in the cold and hot phase, respectively. It thus constitutes a very efficient order parameter, which allows one to determine the transition region at low computational cost. In addition, for open and fixed boundary conditions we address the question of the impact of inhomogeneities and give examples of the reappearance of an energy gap already at moderate lattice sizes.