Indicators of solvability for lattice models

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 de ned complex plane. This latter class cannot therefore be algebraic, nor di erentiably nite nor, when suitably constrained, constructible di erentiably 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.