Two-time Green's function treatment of field-induced quantum criticality of a d-dimensional easy plane ferromagnet with longitudinal uniform interactions

The two-time Green's function equation of motion method is employed to explore the low temperature properties and crossovers close to the field-induced quantum critical point of a d-dimensional spin-1/2 easy-plane ferromagnet with longitudinal uniform interactions. This is performed, on the ground of an exact mapping into an effective XY model in a transverse field, using the Tyablikov decoupling procedure, which is shown to provide, at zero temperature, the exact results recently obtained for the same model with arbitrary d and spin S. We determine the full structure of the phase diagram for different values of d and S = 1/2. Some peculiarities emerge for d ≤ 2 where only an isolated quantum critical point exists. For d > 2 the phase boundary and crossover lines are determined and the physics of the various regions of the phase diagram is found to be consistent with recent renormalization group results. Moreover, for 2 < d < 4 the crossovers near criticality are suitably described in terms of scaling functions and effective critical exponents.