SOLVABILITY OF SOME STATISTICAL-MECHANICAL SYSTEMS

We describe a numerical procedure that clearly indicates whether or no t a given statistical mechanical system is solvable (in the sense of b eing expressible in terms of D-finite functions). If the system is not solvable in this sense, any solution that exists must be expressible in terms of functions that possess a natural boundary. We provide comp elling evidence that the susceptibility of the two-dimensional Ising m odel, the generating function of square lattice self-avoiding walks an d polygons and of hexagonal lattice polygons, and directed animals are in the ''unsolvable'' class.