Divergent Susceptibility of Isotropic Ferromagnets

Abstract

We prove that the susceptibility of an isotropic, two-component, classical vector spin system, e.g., the rigid rotator, diverges in three or four dimensions as the magnetic field $h\to 0$, at all temperatures for which there is a spontaneous magnetization. The divergence is at least as strong as $h^{\frac{1}{2}}$ in three and as $\left|\ln h\right|$ in four dimensions. We also obtain bounds on the rates of exponential decay of the parallel- and transverse-pair correlation functions.