Paramagnetic susceptibility and correlation functions of a d-dimensional classical Heisenberg ferromagnet via the two-time Green function method

In the present paper we investigate the paramagnetic susceptibility and the short-range order correlation functions of a d-dimensional classical isotropic ferromagnetic Heisenberg model with short-range exchange interactions by employing the two-time Green function method in classical statistical mechanics. Here we use Tyablikov–Callen-like decouplings for higher order Green functions and a formula for magnetization recently obtained by extension of the well known Callen method developed many years ago for the quantum isotropic Heisenberg model. Although our analysis is true for any temperature and dimensionality, we focus on one-, and some two- and three-dimensional lattices of experimental interest and derive asymptotic expressions for susceptibility and correlation functions within the paramagnetic phase close to the phase boundary and in the high-temperature regime. Besides, we present a Fourier series expansion method for deriving the high-temperature behaviors of the correlation functions. Our predictions, as obtained from a genuine classical many-body framework, may constitute a good reference point for the quantum counterparts emerging in the classical limit at the same level of approximation. Of course, although the classical spin models have unrealistic properties at sufficiently low temperatures, our classical analysis provides, in a relatively simple way as compared to a quantum treatment, an experimentally interesting scenario at finite temperature and dimensionalities d≥1.