Critical Scattering in a Field and BelowTc

Abstract

Series expansions for spin-spin correlations of simple-cubic, bcc, and square lattice Ising ferromagnets for general field and temperature have been analyzed. To within the attainable precision (of ± 1 to ± 5%) the exponents ${\nu }^{\prime }$ and ${\nu }^c$ are consistent with scaling predictions. Deviations of the scattering from Ornstein-Zernike forms are significantly larger quantitatively than above $T_c$; the second-moment correlation lengths verify $\frac{{{\xi }_1}^{+}}{{{\xi }_1}^{-}\mathrm{}\left(T\right)\mathrm{}}=1.96\mathrm{}\pm 0.03$ as $T\to {T_c}^{\pm }$.