A New Integrable Ising-type Model from 2d N=(2,2) Dualities

2017/08/31 by Shahriyar Jafarzade, Jafarzade, Shahriyar, Zainab Nazari +1 · 1 citation
Mathematics · Physics and Astronomy · #14K25 #16T25 #81T60 #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1709.00070

openalex publication_date 2017/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the equality of 2d N=(2,2) supersymmetric indices in Seiberg-type duality leads to a new integrable Ising-type model. The emergence of the new model is the result of correspondence between the supersymmetric SU(2) quiver gauge theories and the Yang-Baxter equation. Using this correspondence, we solve the star-triangle relation and obtain the two-dimensional exactly solvable spin model. The model corresponding to our solution possesses continuous spin variables on the circle and the Boltzmann weights are demonstrated in terms of Jacobi theta function. Using the solution of the star-triangle relation, we also construct interaction-round-a-face and vertex models.

Citations

• Supersymmetric index on T² x S² and elliptic genus

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• Integrability As Duality: The Gauge/YBE Correspondence

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