Correlation theory of the Heisenberg antiferromagnet and ferromagnet: Dependence on dimension, field, and temperature

The correlation theory is applied to a Heisenberg antiferromagnet in a magnetic field. Special cases covered are the ferromagnet and an anisotropic Heisenberg model. The theory includes selfconsistently correlation effects in static and dynamic properties. It is a generalization of the random-phase approximation and is applicable to the quantum spin case for any dimension and temperature. The static susceptibilities and the excitation spectrum are calculated. Besides the spin-wave excitations a central peak is found which can be understood as coming from local longitudinal fluctuations. The results of the theory are exemplified by numerical calculations for the onedimensional $S=1\mathrm{}$ quantum antiferromagnetic chain. Qualitative agreement is found with computer simulations on a classical chain.