AN IMAGINARY PATH-WEIGHT RANDOM-WALK METHOD FOR CALCULATION ONE-DIMENSIONAL INTERFACE TENSION

We propose an efficient approximation scheme to calculate one-dimensional anisotropic interface tension γ(θ) (θ: interface orientation angle). For a given system, we set up an approximate free random-walk problem where an extra imaginary factor eiϕ/2 is assigned at each turn of the walks, just as in Feynman-Vdovichenko's random-walk solution of the Ising model. We calculate γ(θ) from the lattice Green's function g associated with the random-walk problem. The equilibrium crystal shape is simply given by imaginary poles of g. We apply the method, the imaginary path-weight method, to the hexagonal antiferromagnetic Ising model in a uniform field. We show that, at a particular orientation, the calculated γ(θ) reproduces the accurate solid-on-solid result. The Wulff plot and the equilibrium crystal shape are presented. © 1990, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.