Nonlinear differential equations for the correlation functions of the 2D Ising model on the cylinder
Abstract
Description
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 $τ$-function of Painlevé V).
12 pages, published version (references and comment on boundary conditions added)
12 pages, published version (references and comment on boundary conditions added)