Second-Order Green's-Function Theory of the Infinite-Chain Heisenberg Ferromagnet

Abstract

A second-order self-consistent random-phase-approximation decoupling similar to that used by Kondo and Yamaji for spin-1/2 and by Scales and Gersch for the antiferromagnet is applied to the isotropic infinite-chain Heisenberg ferromagnet for arbitrary spin in zero applied field. At finite temperatures, well-defined spin waves and a finite correlation length are found. In the zero-temperature limit, the correlation length becomes infinite and the exact ground state and spin-wave spectrum are obtained. The correlation functions are isotropic, as required in the absence of magnetization, and are asymptotically exact in the high-temperature limit. Results are compared with extrapolations from finite chains by Bonner and Fisher for spin-1/2 and by Weng for spin 1, and with the rigorous solution by Fisher for the classical infinite-spin limit.