Inversion relations, the Ising model and self-avoiding polygons

Abstract

We develop a numerical technique that enables one to distinguish between those problems whose solution is D-finite and those which are not. We show that the latter class includes the susceptibility of the Ising model, and the self-avoiding walk and polygon generating function on the square and hexagonal lattices. We show that the solution to these problems can only be expressed in terms of functions with natural boundaries.