Green's-Function Theory of an Antiferromagnet

Abstract

A Green's-function theory is developed for a Heisenberg antiferromagnet using a decoupling scheme which conserves the frequency moments of the spectral function. The method closely follows Tahir-Kheli's decoupling scheme for a ferromagnetic system, and various correlation functions, sublattice magnetization, and susceptibilities are obtained. The theory is compared with the low- and high-temperature series expansions. The N\'eel temperature obtained using the theory is used to estimate $\frac{|J|}{{k}_{B}}$ values of some transition-metal compounds. The theory is then applied to one and two dimensions, and it is found to lend support to Stanley and Kaplan's suggestion of a second-order phase transition, while not predicting spontaneous magnetic ordering.