Orientation Dependence of Surface Critical Phenomena in Antiferromagnets: Exact Results in Two Dimensions

For an Ising antiferromagnet, we analyze exact expressions for the one- and two-point correlation functions for spins on the edge of a square lattice with a magnetic field applied to the surface sites. Two different edge orientations, with respect to the crystal axes, are treated. At bulk criticality, we confirm that the surface universality class depends on the edge orientation and show the importance of having the bulk phase in a pure state. For the two-point function, we find a singularity in the correlation length due to depinning effects which we argue is also present in higher dimensions.