Multiple phase coexistence and the scaling transformation

It is shown that a simple extension of the finite size scaling method in the theory of critical phenomena can yield a sequence of approximants to any point subset of the interaction parameter space where multiple phase coexistence is possible. The method is illustrated by an application to the three-, four- and five-state Potts models, and even in its lowest order of approximation is able to distinguish the difference in the zero-field critical behaviour between the five-state and the three- and four-state models.