Nonlinear differential equations for the correlation functions of the 2D Ising model on the cylinder

Abstract

We derive determinant representations and nonlinear differential equations for the scaled 2-point functions of the 2D Ising model on the cylinder. These equations generalize well-known results for the infinite lattice (Painlevé III equation and the equation for the $\tau$-function of Painlevé V).

12 pages, published version (references and comment on boundary conditions added)

References in corpus (2)

• Differential Equations for Sine-Gordon Correlation Functions at the Free Fermion Point
• On the Solution of a Painlevé III Equation