Scaling functions in the square Ising model

Abstract

We show and give the linear differential operators of order , for the integrals which appear in the two-point correlation scaling function of Ising model . The integrals are given in expansion around in the basis of the formal solutions of with transcendental combination coefficients. We find that the expression is a solution of the Painlevé VI equation in the scaling limit. Combinations of the (analytic at ) solutions of sum to . We show that the expression is the scaling limit of the correlation function and . The differential Galois groups of the factors occurring in the operators are given.