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

Sulejmanpasic, Tin (2021) 'Ising model as a U(1) lattice gauge theory with a θ -term.', Physical Review D, 103 (3). 034512.


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.

Item Type:Article
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Publisher statement:Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP
Date accepted:25 January 2021
Date deposited:21 September 2021
Date of first online publication:25 February 2021
Date first made open access:21 September 2021

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