Simulating the All-Order Strong Coupling Expansion V: Ising Gauge Theory

TL;DR

This paper develops an exact reformulation of Z(2) lattice gauge theory as a random surface model, enabling efficient Monte Carlo simulations of Polyakov line correlators and boundary effects, with results compared to string theory predictions.

Contribution

It introduces a novel surface-based simulation method for Z(2) gauge theory, extending worm algorithms to include Polyakov line defects and enabling precise measurements of correlators and boundary effects.

Findings

Polyakov line correlators measured with small errors independent of separation

Effective string theory predictions are validated against simulation results

Method applicable in any dimension, demonstrated in three dimensions

Abstract

We exactly rewrite the Z(2) lattice gauge theory with standard plaquette action as a random surface model equivalent to the untruncated set of its strong coupling graphs. By extending the worm approach applied to spin models we simulate such surfaces including Polyakov line defects that randomly walk over the lattice. Our Monte Carlo algorithms for the graph ensemble are reasonably efficient but not free of critical slowing down. Polyakov line correlators can be measured in this approach with small relative errors that are independent of the separation. As a first application our results are confronted with effective string theory predictions. In addition, the excess free energy due to twisted boundary conditions becomes an easily accessible observable. Our numerical experiments are in three dimensions, but the method is expected to work in any dimension.