Exact Relation for Magnon Theories of Magnetism and its Consequences in Calculations of Magnon Specific Heats

Abstract

A proof is given that the expectation value of the Heisenberg exchange Hamiltonian for ferromagnetism can be computed exactly, knowing only the spectral function for the transverse correlation functions. The proof is readily extended to Ising and Dyson theories of magnetism, and to ferrimagnets of $n$ sublattices. Application to calculations of magnon specific heats shows that special care is required when approximate magnon spectra are used to evaluate the exact relation.