# U(1) Gauge Theory with Villain Action on Spherical Lattices

## TL;DR

This study investigates the phase transition behavior of U(1) gauge theory with Villain action on spherical lattices, revealing a nontrivial second order transition with specific critical exponents.

## Contribution

It provides the first finite-size scaling analysis of U(1) gauge theory with Villain action on spherical lattices, identifying a non-Gaussian critical exponent.

## Key findings

- No 2-state signal in plaquette distribution at transition
- Finite-size scaling indicates second order phase transition
- Critical exponent nu = 0.366(12) suggests nontrivial continuum limit

## Abstract

We have studied the U(1) gauge field theory with Villain (periodic Gaussian) action on spherelike lattices. The effective size of the systems studied ranges from 6 to 16. We do not observe any 2-state signal in the distribution function of the plaquette expectation value at the deconfining phase transition. The observed finite-size scaling behavior is consistent with a second order phase transition. The obtained value of the critical exponent is nu =0.366(12) and thus neither Gaussian (nu = 0.5) nor discontinuous (nu=0.25) type, indicating a nontrivial continuum limit.