A new solution of the star-triangle relation

TL;DR

This paper introduces a novel solution to the star-triangle relation for an Ising-type model featuring two types of spins, with weights expressed via the gamma function, ensuring real and positive values.

Contribution

The paper presents a new explicit solution to the star-triangle relation for a complex spin model with continuous and discrete variables, expanding integrable models in statistical mechanics.

Findings

Boltzmann weights are real and positive

Weights depend on sums and differences of spins

Solution involves Euler gamma function

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.