The internal energies of Heisenberg magnetic systems

Abstract

The internal energies, including transverse and longitudinal parts, of quantum Heisenberg systems for arbitrary spin S are investigated by the double-time Green's function method. The expressions for ferromagnetic (FM) and antiferromagnetic (AFM) systems are derived when one component of magnetization is considered with the higher order longitudinal correlation functions being carefully treated. An unexpected result is that around the order and disorder transition points the neighboring spins in a FM (AFM) system are more likely longitudinally antiparallel (parallel) than parallel (antiparallel) to each other for S<=3/2 in spite of the FM (AFM) exchange between the spins. This is attributed to the strong quantum fluctuation of the systems with small S values. We also present the expressions of the internal energies of FM systems when the three-component of magnetizations are considered.