MAGNETIC-PROPERTIES OF QUANTUM HEISENBERG FERROMAGNETS WITH LONG-RANGE INTERACTIONS

Quantum Heisenberg ferromagnets with long-range interactions in low dimensions are investigated by means of the Green's function method. The model Hamiltonian is given by H = -(J(o)/2) Sigma(i not equal j)r(ij)(-p)S(i) . S-j-H Sigma(j)S(j)(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 pi 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.