Behavior of Two-Point Correlation Functions Near and on a Phase Boundary

The asymptotic decay of the two-point correlation function GAB(→R) at and near a phase-separation point is discussed for d-dimensional, spin-{} Ising models at low temperature. The general behavior, even on the phase boundary ($H=0$), is in agreement with extended Ornstein-Zernike predictions. It is shown why the nearest-neighbor two-dimensional model in zero field is an exception. The decay of GAB(→R₁,→R₂) near a free surface at high temperatures agrees with phenomenological predictions using a vanishing boundary condition. At low temperature, however, the decay of correlation near a surface is exponentially slower than in the bulk.