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

Abstract

The asymptotic decay of the two-point correlation function $G_{\mathrm{AB}}\left(\overrightarrow{\mathrm{R}}\right)$ at and near a phase-separation point is discussed for $d$-dimensional, spin-½ Ising models at low temperature. The general behavior, even on the phase boundary ($H=0\mathrm{}$), 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 $G_{\mathrm{AB}}({\overrightarrow{\mathrm{R}}}_1,{\overrightarrow{\mathrm{R}}}_2)$ 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.