Singularities and Scaling Functions at the Potts-Model Multicritical Point

Differential renormalization equation for the $q$-state Potts model are proposed, and the critical behavior of the model near $q={q}_{c}$ discussed. The equations give rise to critical and tricritical fixed points which merge at $q={q}_{c}$ when a dilution field becomes marginal, to an essential singularity in the latent heat as a function of $q={q}_{c}$, in accordance with the exact result of Baxter, and, for $q={q}_{c}$, to a logarithm correction to the power-law behavior of the free energy as a function of $T\ensuremath{-}{T}_{c}$.