Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs

Understand

In this paper we give an overview of exactly solved edge-interaction models, where the spins are placed on sites of a planar lattice and interact through edges connecting the sites.

• We only consider the case of a single spin degree of freedom at each site of the lattice.
• The Yang-Baxter equation for such models takes a particular simple form called the star-triangle relation.
• Interestigly all known solutions of this relation can be obtained as particular cases of a single "master solution", which is expressed through the elliptic gamma function and have continuous spins taking values of the circle.