From dual gauge theories to dual spin models

TL;DR

The review addresses the problem of generating new exactly solvable lattice spin models by leveraging the gauge/YBE correspondence, which ties dual supersymmetric gauge theories to Yang–Baxter equation solutions. It surveys core integrability relations—the star–triangle and star–star relations—and shows how dualities in supersymmetric gauge theories yield explicit Boltzmann weights for these relations. It then details dual spin-model constructions, including decoration, flipping, star-square, and generalized star-triangle transformations, and explains how these operations map Ising-like models to decorated or non-planar lattices while preserving integrability. Overall, the paper presents a unified framework that connects high-energy dualities to statistical-mechanics integrability, enabling systematic discovery of new exactly solvable models on broader lattice geometries and informing future research through explicit dual pairs and special-function solutions.

Abstract

This brief review surveys recent progress driven by the gauge/Yang-Baxter equation (YBE) correspondence. This connection has proven to be a powerful tool for discovering novel integrable lattice spin models in statistical mechanics by exploiting dualities in supersymmetric gauge theories. In recent years, research has demonstrated the use of dual gauge theories to construct new lattice spin models that are dual to Ising-like models.