2018/12/07 by Changnan Peng, Peng, Changnan
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1812.02938
openalex publication_date 2018/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that the normal three-dimensional (3D) Ising model on a cubic lattice is dual to the Wegner's 3D Z2 lattice gauge theory. Here we find an unusual Z2 lattice gauge theory which is dual to the 3D Ising model with not only nearest-neighbor (nn) coupling, but also next-nearest-neighbor (nnn) coupling. Our gauge theory has on each edge four Z2 variables that have product +1, each located on a vector perpendicular to the edge. The nn coupling in the Ising model maps to the plaquette term in the gauge theory where the four variables multiplied have their vectors pointing inward, while the nnn coupling maps to the coupling between the Z2 variables on nearby vectors on each edge in the gauge theory. A Wilson loop observable in the gauge theory depends on a framing of a loop, and maps to a surface of flipped-sign nn and nnn couplings in the Ising model. Further numerical simulations could be made to explore the universality at the phase transition.