Two-dimensional elastic lattice model with spontaneous stress

A two-dimensional elastic lattice model with spontaneous stress is numerically simulated and compared with the continuum elasticity theory. Two adatoms separated by a distance x interact repulsively with an x^-2 potential in agreement with continuum theory, but the strength of the interaction is about half of the theoretical prediction due to the relaxation of the adatom position as well as substrate atoms. Repulsive interaction between two step edges of the same sign is also proportional to x^-2, but with a coupling strength much larger than the continuum elasticity, because forces are distributed not on a single plane but on two layers. The same reason leads to a great discrepancy in the interaction between steps with the opposite signs. Even though the continuum elasticity predicts no interaction, they seem to interact repulsively with the same x^-2 dependence. Between step edges on the groove, the interaction is apparently long-ranged, proportional to x^-1.5.