# Four-dimensional pure compact U(1) gauge theory on a spherical lattice

## TL;DR

This study explores the phase transition in a 4D pure compact U(1) gauge theory on spherical lattices, revealing a likely second-order transition with specific critical exponents and overcoming previous lattice study challenges.

## Contribution

It introduces a spherical lattice approach for studying the 4D U(1) gauge theory, enabling clearer analysis of the phase transition and critical behavior.

## Key findings

- Absence of two-state signal on spherical lattices for gamma ≤ 0
- Finite-size scaling behavior with correlation length exponent nu ≈ 0.365
- Phase transition likely of second order in the universality class of a non-Gaussian fixed point

## Abstract

We investigate the confinement-Coulomb phase transition in the four-dimensional (4D) pure compact U(1) gauge theory on spherical lattices. The action contains the Wilson coupling beta and the double charge coupling gamma. The lattice is obtained from the 4D surface of the 5D cubic lattice by its radial projection onto a 4D sphere, and made homogeneous by means of appropriate weight factors for individual plaquette contributions to the action. On such lattices the two-state signal, impeding the studies of this theory on toroidal lattices, is absent for gamma le 0. Furthermore, here a consistent finite-size scaling behavior of several bulk observables is found, with the correlation length exponent nu in the range nu = 0.35 - 40. These observables include Fisher zeros, specific-heat and cumulant extrema as well as pseudocritical values of beta at fixed gamma. The most reliable determination of nu by means of the Fisher zeros gives nu = 0.365(8). The phase transition at gamma le 0 is thus very probably of 2nd order and belongs to the universality class of a non-Gaussian fixed point.