QUANTUM HEISENBERG-MODEL WITH LONG-RANGE FERROMAGNETIC INTERACTIONS

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) [H = -1/2SIGMA(i not-equal j)(J0/r(ij)p)S(i).S(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 alpha + 1 = gamma-1 when 2 < p < 3.