Singularities and Scaling Functions at the Potts-Model Multicritical Point

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