  We study a force-based hybrid method that couples atomistic model with
Cauchy-Born elasticity model with sharp transition interface. We identify
stability conditions that guarantee the convergence of the hybrid scheme to the
solution of the atomistic model with second order accuracy, as the ratio
between lattice parameter and the characteristic length scale of the
deformation tends to zero. Convergence is established for hybrid schemes with
planar sharp interface for system without defects, with general finite range
atomistic potential and simple lattice structure. The key ingredient of the
proof is regularity and stability analysis of elliptic systems of difference
equations. We apply the results to atomistic-to-continuum scheme for a 2D
triangular lattice with planar interface.
