The analytic structure of lattice models - Why can't we solve most models?

Abstract

We investigate the solvability of a variety of well-known problems in lattice statistical mechanics. We provide a new numerical procedure which enables one to conjecture whether the solution falls into a class of functions calleddifferentiably finite functions. Almost all solved problems fall into this class. The fact that one can conjecture whether a given problem is or is not D-finite then informs one as to whether the solution is likely to be tractable or not. We also show how, for certain problems, it is possible to prove that the solutions are notD-finite, based on the work of Rechnitzer [1–3].