Compact U(1) Gauge Theory on Lattices with Trivial Homotopy Group

TL;DR

This paper investigates a pure gauge U(1) lattice model on a manifold with trivial homotopy, revealing how topology influences monopole fluctuations and phase transition signals.

Contribution

It introduces a new lattice geometry with trivial homotopy and analyzes its effects on monopole loops and phase transition signals compared to traditional setups.

Findings

Monopole loops can fluctuate freely without boundary restrictions.

The two-state signal in energy distribution disappears in the new geometry.

No consistent finite size scaling behavior is observed.

Abstract

We study the pure gauge model on a lattice manifold with trivial fundamental homotopy group, homotopically equivalent to an $S_4$. Monopole loops may fluctuate freely on that lattice without restrictions due to the boundary conditions. For the original Wilson action on the hypertorus there is an established two-state signal in energy distribution functions which disappears for the new geometry. Our finite size scaling analysis suggests stringent upper bounds on possible discontinuities in the plaquette action. However, no consistent asymptotic finite size scaling behaviour is observed.