Behavior of Two-Point Correlation Functions at High Temperatures

Abstract

The asymptotic decay of the general two-point correlation function $G_{\mathrm{AB}}\left(\overrightarrow{R}\right)$ at high temperatures is analyzed on the basis of the $d$-dimensional, spin-½ Ising model in general field $H$. For $H\ne 0$ the Ornstein-Zernike form $\approx \frac{D_A{D}_B{e}^{-\kappa R}}{R^{\frac{\mathrm{}(d-1\mathrm{})\mathrm{}}{2}}}$ is found for general $\hat{A}$ and $\hat{B}$. However for certain operators, including the energy, the amplitude of the Ornstein-Zernike term vanishes as $H^2$ and in zero field only the higher order decay $\sim \frac{e^{-2\mathrm{}\kappa R}}{R^d}$ remains. The relation to approximate treatments and to critical-point phenomena is discussed briefly.