Quantum criticality of a d-dimensional spin-S XXZ ferromagnetic model with longitudinal infinite-range interactions

A d-dimensional spin-S XXZ ferromagnetic model with uniform long-range interactions in the z-direction is mapped into an effective XY model in a transverse field. Then, using the two-time Green function equation of motion method, the zero-temperature properties for a periodic cubic lattice are exactly obtained close to the quantum critical point signaling the field-induced quantum phase transition from the fully polarized state into a phase with easy-plane spin ordering. We determine the relevant critical exponents which have a mean-field character for any d and S.