A modified spin-wave theory is applied to the one- and two-dimensional quantum Heisenberg model with long-range ferromagnetic interactions proportional to r^-p[scrH=-1/2tsum_i≠j (J₀/rᵢⱼᵖ)Sᵢ{·}Sⱼ]. It is shown that for dp2d 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=γ^-1 when 2p3.
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Nakano et al. (1994) studied this question.
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