Anisotropic interfacial tension and the equilibrium crystal shape of Kagomé-lattice eight-vertex model

Abstract

We exactly calculate the anisotropic interfacial tension of the Kagome-lattice eight-vertex model with the help of two types of square-lattice models. Each square-lattice model is inhomogeneous but still possesses a one-parameter family of commuting transfer matrices. From the anisotropic interfacial tension, the equilibrium shape of an inclusion of one ordered phase in an environment of another is obtained by applying the Wulff construction. Calculations are expressed by the use of differential forms on a Riemann surface of genus 1; and the equilibrium shape is written as an elliptic curve. We suggest the possibility of interpreting critical phenomena in terms of the moduli space of Riemann surfaces of genus 1.