A new solution of the star-triangle relation

Abstract

We obtain a new solution to the star-triangle relation for an Ising-type model with two kinds of spin variables at each lattice site, taking continuous real values and arbitrary integer values, respectively. The Boltzmann weights are manifestly real and positive. They are expressed through the Euler gamma function and depend on sums and differences of spins at the ends of the edge.

6 pages, 1 figure; v2: corrected typos, minor changes and improvements to text

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Cited by in corpus (14)

• New solutions of the star-triangle relation with discrete and continuous spin variables
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• The star-triangle relation and 3d superconformal indices
• Elliptic hypergeometric sum/integral transformations and supersymmetric lens index
• Basic hypergeometry of supersymmetric dualities
• On Complex Gamma-Function Integrals
• The Endless Beta Integrals
• Barnes-Ismagilov integrals and hypergeometric functions of the complex field
• Integrable lattice spin models from supersymmetric dualities
• $\mathrm{SL}(2,\mathbb{C})$ Gustafson Integrals
• Exactly solved models on planar graphs with vertices in ${\mathbb{Z}}^3$
• An analog of the Dougall formula and of the de Branges--Wilson integral
• Two-component Yang-Baxter maps and star-triangle relations
• On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions