The eight-vertex model and Painleve VI

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.

9 pages, LaTeX, submitted to the special issue on Painleve VI, Journal of Physics A

Cited by in corpus (12)

• Analytic theory of the eight-vertex model
• Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2
• Spin chains with dynamical lattice supersymmetry
• Holonomy of the Ising model form factors
• Ground-state properties of a supersymmetric fermion chain
• New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
• The TQ equation of the 8 vertex model for complex elliptic roots of unity
• The nineteen-vertex model and alternating sign matrices
• Fuchs versus Painlevé
• A staggered fermion chain with supersymmetry on open intervals
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder
• Free Energy of the Eight Vertex Model with an Odd Number of Lattice Sites