Quantum-Field-Theory Approach to the Heisenberg Ferromagnet

Abstract

Earlier derivations of simple Wick's theorems for operators of spin ½ and 1 (in units of $\hslash$) using the drone-fermion representation are applied to the Heisenberg model. The resulting diagrammatic-perturbational approach (Green's functions) is carried out in both the high- and low-temperature domains, where the expansion criteria of Stinchcombe et al. are closely followed. The present work effectively reexpresses the semi-invariant analysis of these authors in a much simpler manner, and many of their results are straight-forwardly reproduced. The use of standard quantum-field-theory techniques enables renormalization to be undertaken in a simple, systematic manner. At low temperatures the present fermion analysis gives Dyson's $T^4$ contribution to the free energy from the first Born approximation to spin-wave scattering. Higher-order spin-wave contributions give a damping term, which, upon evaluation in the lowest approximation, is identical to that found by ter Haar and Tahir-Kheli.