# Critical behavior and monopole density in U(1) lattice gauge theory

## TL;DR

This paper investigates how the order of phase transitions in 4D U(1) lattice gauge theory changes with monopole coupling, showing a shift from first to second order and analyzing critical exponents and monopole density behavior.

## Contribution

It demonstrates that increasing monopole coupling leads to a second-order transition with a distinct critical exponent, and explores the persistence of the phase transition at large negative couplings.

## Key findings

- Transition becomes second order at high monopole coupling
- Critical exponent differs from Gaussian case
- Monopole density becomes constant in the second order region

## Abstract

Our study of the energy distribution has shown that the strength of the first order transition in the four-dimensional compact U(1) lattice gauge theory decreases when the coupling $\lambda$ of the monopole term increases. The disappearance of the energy gap for sufficiently large values of $\lambda$ indicates that the transition ultimately becomes of second order. In our present investigation, based on a finite-size analysis, we show that already at $\lambda= 0.9$ the critical exponent is characteristic of a second-order transition. Interestingly, this exponent turns out to be definitely different from that of the Gaussian case. We observe that the monopole density becomes constant in the second order region. In addition we find the rather surprising result that the phase transition persists up to very large values of $\lambda$, where the transition moves to (large) negative $\beta$.