The eight-vertex model and Painleve VI

TL;DR

This paper links special elliptic solutions of Painleve VI to solutions of the non-stationary Lame equation, which are relevant for understanding the ground state of Baxter's eight-vertex model at a specific parameter.

Contribution

It establishes a novel connection between Painleve VI solutions and the eight-vertex model's ground state properties at a special parameter value.

Findings

Identifies a link between Painleve VI elliptic solutions and the non-stationary Lame equation.

Connects these mathematical solutions to the physical properties of the eight-vertex model.

Provides insight into the model's behavior at the disordered regime point =b3/3.

Abstract

In this letter we establish a connection of Picard-type elliptic solutions of Painleve VI equation with the special solutions of the non-stationary Lame equation. The latter appeared in the study of the ground state properties of Baxter's solvable eight-vertex lattice model at a particular point, $\eta=\pi/3$, of the disordered regime.