  We study a two-dimensional honeycomb lattice gas model with both nearest- and
next-nearest-neighbor interactions in a staggered field, which describes the
surface of stoichiometrically binary crystal.
  We calculate anisotropic step tension, step stiffness, and equilibrium island
shape, by an extended random walk method. We apply the results to Si(111)
7$\times$7 reconstructed surface and high-temperature Si(111) 1$\times$1
surface. We also calculate inter-step interaction coefficient.
