Scaling theory of the Potts-model multicritical point

Abstract

A theory of the scaling behavior near the ${q}_{c}=4$ state multicritical point of the two-dimensional Potts lattice gas model is developed. Proceeding from the assumption that a dilution field becomes marginal at the multicritical point while the thermal and ordering fields are relevant, a set of differential renormalization group (RG) equations for these fields are constructed. Keeping terms through second order we find that these equations are characterized by five universal parameters which we evaluate using exact as well as conjectured results. Based upon these RG equations, we investigate the physical properties of the two-dimensional Potts lattice gas for $q$ near ${q}_{c}$. For the pure Potts model with $q={q}_{c}$ we find logarithmic temperature corrections to the specific heat and the spontaneous magnetization. At ${T}_{c}$ we find $\mathrm{ln}(r)$ corrections to the power law behavior of the spin-spin correlation function. For the dilute Potts model with $q={q}_{c}$ we find that the latent heat, the discontinuity in the magnetization, and the discontinuity in the coexisting densities vanish with an essential singularity as $T$ approaches the multicritical point from the first-order side. Results for $q>{q}_{c}$ and $q<{q}_{c}$ are also given.