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

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.

25 pages, 7 figures, V2: small changes in the text, refs. added, new footnote p.18, to appear in Nucl. Phys. B [FS]

References in corpus (7)

• Monte Carlo simulation of the SU(3) spin model with chemical potential in a flux representation
• Method for simulating O(N) lattice models at finite density
• Simulating the All-Order Strong Coupling Expansion I: Ising Model Demo
• Surface worm algorithm for abelian Gauge-Higgs systems on the lattice
• On the intrinsic width of the chromoelectric flux tube in finite temperature LGTs
• Worm Monte Carlo study of the honeycomb-lattice loop model
• Gauge and matter fields as surfaces and loops - an exploratory lattice study of the Z(3) Gauge-Higgs model

Cited by in corpus (6)

• Approaches to the sign problem in lattice field theory
• Solving the sign problems of the massless lattice Schwinger model with a dual formulation
• Dual simulation of the 2d U(1) gauge Higgs model at topological angle $\theta =\pi$: Critical endpoint behavior
• Simulation strategies for the massless lattice Schwinger model in the dual formulation
• The worm process for the Ising model is rapidly mixing
• A Geometric Monte Carlo Algorithm for the Antiferromagnetic Ising model with "Topological" Term at $\theta =\pi$