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.

arXiv comment9 pages, LaTeX, submitted to the special issue on Painleve VI, Journal of Physics A

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• 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
• The eight-vertex model and lattice supersymmetry
• Holonomy of the Ising model form factors
• A possible combinatorial point for XYZ-spin chain
• Exact and simple results for the XYZ and strongly interacting fermion chains
• Ground-state properties of a supersymmetric fermion chain
• Special polynomials related to the supersymmetric eight-vertex model: A summary
• Finite size emptiness formation probability of the XXZ spin chain at $\Delta =-1/2$
• The TQ equation of the 8 vertex model for complex elliptic roots of unity
• New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
• On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions
• The nineteen-vertex model and alternating sign matrices
• A staggered fermion chain with supersymmetry on open intervals
• On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions
• Fuchs versus Painlevé
• Elliptic pfaffians and solvable lattice models
• Integrable structure of products of finite complex Ginibre random matrices
• A Combinatorial Description of Certain Polynomials Related to the XYZ Spin Chain
• Sum rules for the supersymmetric eight-vertex model
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder
• Six-vertex model and non-linear differential equations I. Spectral problem
• Free Energy of the Eight Vertex Model with an Odd Number of Lattice Sites
• A Combinatorial Description of Certain Polynomials Related to the XYZ Spin Chain. II. The Polynomials $p_n$