  The quantitative knowledge of interface anisotropy in lattice models is a
major issue, both for the parametrization of continuum interface models, and
for the analysis of experimental observations. In this paper, we focus on the
anisotropy of line tension and stiffness, which plays a major role both in
equilibrium shapes and fluctuations, and in the selection of nonequilibrium
growth patterns. We consider a 2D Ising Hamiltonian on a square lattice with
first and second-nearest-neighbor interactions. The surface stiffness and line
tension are calculated by means of a broken-bond model for arbitrary
orientations. The analysis of the interface energy allows us to determine the
conditions under which stiffness anisotropy is minimal. These results are
supported by a quantitative comparison with kinetic Monte Carlo simulations,
based on the coupling of a field of mobile atoms to a condensed phase.
Furthermore, we introduce a generic smoothing parameter which allows one to
mimic the finite resolution of experimental microscopy techniques. Our results
provide a method to fine-tune interface energy in models of nanoscale
non-equilibrium processes, where anisotropy and fluctuations combine and give
rise non-trivial morphologies.
