2020/09/30 by Tin Sulejmanpašić, Tin Sulejmanpasic · 10 citations
Mathematics · Physics and Astronomy · #Combinatorics #Duality (order theory) #Gauge theory #Ising model #Lattice (music) #Lattice field theory #Lattice gauge theory #Mathematical physics #Mathematics #Phase (matter) #Phase diagram #Physics #Quantum Chromodynamics and Particle Interactions #Quantum many-body systems #Quantum mechanics #Statistical physics #Term (time) #Theoretical and Computational Physics #cond-mat.stat-mech #hep-lat #hep-th
paper · pdf · doi:10.1103/physrevd.103.034512
published in Physical review. D/Physical review. D. 103(3) (American Physical Society) · 6 pages, 2 figures. This version corrected a typo in the text and split Fig.2 into a) and b) part
openalex created_date 2020/10/01 · arxiv created 2021/02/04 · openalex publication_date 2021/02/25 · arxiv updated 2021/03/03 · openalex updated_date 2026/08/05
We discuss a gauged XY model a \ensuremathθ-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.