Equilibrium crystal shape of the Potts model at the first-order transition point

We investigate the Q-state two-dimensional Potts model. The anisotropic interfacial tension is related by duality to the anisotropic correlation length. For Q > 4 we calculate exactly the anisotropic correlation length at the first-order transition point. From the calculated anisotropic correlation length, the equilibrium crystal shape (ECS) is derived via the Wulff construction. The ECS is expressed by means of a simple algebraic curve. Regarding Q as a temperature scale, we show that the Potts model has the same ECS as the eight-vertex model. We discuss a connection between the ECS and the q-deformed pseudo-Euclidian algebra.