Ising model as a U(1) lattice gauge theory with a θ -term

Sulejmanpasic, Tin

Abstract

We discuss a gauged XY model a θ -term on an arbitrary lattice in 1 + 1 dimensions and show that the theory reduces exactly to the 2d Ising model on the dual lattice in the limit of the strong gauge coupling, provided that the topological term is defined via the Villain action. We discuss the phase diagram by comparing the strong and weak gauge coupling limits and perform Monte Carlo simulations at intermediate couplings. We generalize the duality to higher-dimensional Ising models using higher-form U(1) gauge field analogs.

Citation

Sulejmanpasic, T. (2021). Ising model as a U(1) lattice gauge theory with a θ -term. Physical Review D, 103(3), Article 034512. https://doi.org/10.1103/physrevd.103.034512

• Journal Article Type: Article
• Acceptance Date: Jan 25, 2021
• Online Publication Date: Feb 25, 2021
• Publication Date: Feb 1, 2021
• Deposit Date: Sep 21, 2021
• Publicly Available Date: Sep 21, 2021
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 103
• Issue: 3
• Article Number: 034512
• DOI: https://doi.org/10.1103/physrevd.103.034512
• Public URL: https://durham-repository.worktribe.com/output/1234049