Quantum Heisenberg ferromagnets with long-range interactions in low dimensions are inves- tigated by means of the Green’s frunction method. The model Hamiltonian is given by scrH=-(${\mathit{J}}_0$/2)${\mathcal{J}}_{\mathit{i}\mathrm{\ne }\mathit{j}}$${\mathit{r}}_{\mathit{i}\mathit{j}}^{\mathrm{-}\mathit{p}}$${\mathbf{S}}_{\mathit{i}}$⋅${\mathbf{S}}_{\mathit{j}}$ -H${\mathcal{J}}_{\mathit{j}}$${\mathit{S}}_{\mathit{j}}^{\mathit{z}}$. It is shown that there exists a finite-temperature phase transition in the region d<p<2d for the d-dimensional case and that no transitions at any finite temperature exist for p≥2d; the critical temperature is also estimated. We study the magnetic properties of this model. We calculate the critical exponents’ dependence on p; these exponents also satisfy a scaling relation. Some of the results were also found using the modified spin-wave theory and are in remarkable agreement with each other.

• Received 3 March 1995

DOI:https://doi.org/10.1103/PhysRevB.52.6606