Reply to 'Comment on "Equilibrium crystal shape of the Potts model at the first-order transition point"'

The eight-vertex model is defined on the square lattice rotated through an arbitrary angle with respect to the coordinate axes. We re-examine the analysis of the anisotropic correlation length in a previous paper (Fujimoto M 1996 Physica A 233 485-502). We point out that the asymptotic form of the correlation function is expressed by the use of differential forms on a Riemann surface of genus 1. Combined with the symmetry of the square lattice, this fact explains that the anisotropic correlation length is represented in terms of simple algebraic curves. The argument is applicable to a wide class of lattice models (including unsolvable ones).