Leading corrections to the scaling function on the diagonal for the two-dimensional Ising model

Abstract

In the neighbourhood of the critical point, the correlation length of the spin-spin correlation function of the two-dimensional Ising model diverges. The correlation function permits a scaling limit in which the separation N between spins goes to infinity, but the scaling variable remains fixed, where t is the coupling, and t = 1 the critical point. Previous work has specified these scaling functions (there is one for the critical point being approached from above, and another if approached from below) in terms of transcendents defined by a particular -form of the degenerate Painlevé V equation. For the diagonal-diagonal correlation, we characterise the first two leading large N correction t..