A modified spin-wave theory is applied to the one- and two-dimensional quantum Heisenberg model with long-range ferromagnetic interactions proportional to ${\mathit{r}}^{\mathrm{-}\mathit{p}}$[scrH=-1/2${\mathit{tsum}}_{\mathit{i}\mathrm{\ne }\mathit{j}}$ (${\mathit{J}}_0$/${\mathit{r}}_{\mathit{i}\mathit{j}}^{\mathit{p}}$)${\mathbf{S}}_{\mathit{i}}$⋅${\mathbf{S}}_{\mathit{j}}$]. It is shown that for d<p<2d there exists a phase transition at finite temperatures; the critical temperature is estimated. The susceptibility and the specific heat are obtained at low temperatures. Our results for d=1, p=2, and S=1/2 agree with the exact solution of the Haldane-Shastry model. For d=1, we find a scaling relation α+1=${\gamma }^{\mathrm{-}1}$ when 2<p<3.

• Received 13 June 1994

DOI:https://doi.org/10.1103/PhysRevB.50.10331