Elastic interaction in a two-dimensional discrete lattice model

We introduce a two-dimensional lattice model with elastic deformations and calculate numerically the interaction energy between force distributions localized on a surface. In particular, the interaction between adatoms and that between steps are evaluated by the use of corresponding force distributions, and the result is compared with the continuum elasticity theory where surface defects are replaced by force dipoles placed on a flat surface. The continuum theory agrees with the simulation result asymptotically when the surface is flat, but it does not when there are steps on the surface. Steps with the same sign interact with the power la iv r(-2) in agreement with the continuum theory, but its strength is about ten times larger than the theoretical one. The interaction between steps with the opposite signs shows an apparent discrepancy: the power-law interaction with noninteger exponents in the simulation whereas no interaction in the continuum elasticity theory.