Exact Relations among Amplitudes at Critical Points of Marginal Dimensionality

A renormalization-group analysis of a three-dimensional Ising model with dipolar forces establishes a relation between the specific heat and the correlation length, in the limit t=(T-Tc)Tc→0. Specific-heat data are used to predict ζ~1.41t^-1/2|lnt|1/6 {} for LiTbF₄. A relation among the magnetization, the specific heat, and the susceptibility is also given. Similar relations are found for n-component short-range models at $d=4$ and d=4-ε.