Ising model as a $U(1)$ Lattice Gauge Theory with a $\theta$-term
High Energy Physics - Lattice
2021-03-03 v3 Statistical Mechanics
High Energy Physics - Theory
Abstract
We discuss a gauged XY model a -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 analogues.
Keywords
Cite
@article{arxiv.2009.13383,
title = {Ising model as a $U(1)$ Lattice Gauge Theory with a $\theta$-term},
author = {Tin Sulejmanpasic},
journal= {arXiv preprint arXiv:2009.13383},
year = {2021}
}
Comments
6 pages, 2 figures. This version corrected a typo in the text and split Fig.2 into a) and b) part