Abstract :
We present a numerical method, based on exact series expansions, that distinguishes between lattice-based models both in combinatorics and statistical mechanics that are likely to be solvable in terms of simple functions of mathematical physics, and those that possess a natural boundary in a suitably defined complex plane. This latter class cannot therefore be algebraic, nor differentiably finite nor, when suitably constrained, constructible differentiably algebraic. Known solutions in this latter class are all expressed as modular functions with a particular choice of variable or as q-generalisations of standard functions.
