An exact solution to the classical,anisotropic Heisenberg model with long-range Kac interactions

A rigorous derivation is given for the “constant-magnetization” free energy density of the classical, anisotropic Heisenberg model with long-range Kac interactions. The derivation involves bounding arguments similar to those used for a classical fluid by Lebowitz and Penrose. The present work is carried out in a constant-magnetization ensemble. The free energy density is determined exactly under a quadruple-limiting process. The limits involved are a Lebowitz-Penrose type of triple-limiting process, followed by a final limit,x→ 0, wherex is a parameter which represents the range over which each component of the net spin density can vary. Explicit equations of state are determined for the special case of zero short-range interactions plus pure Kac-type long-range interactions.