Field-induced quantum critical point in planar Heisenberg ferromagnets with long-range interactions: Two-time Green’s function framework

The two-time Green’s function method is used to study the critical properties and crossover phenomena near the field-induced quantum critical point (QCP) of a d-dimensional spin-S planar Heisenberg ferromagnet with long-range interactions decaying as r−α (with α>d) with the distance r between spins. We adopt the Callen scheme for spin S and the Tyablikov decoupling procedure which is expected to provide suitable results at low temperatures. Different quantum critical regimes are found in the (α,d) plane and the global structure of the phase diagram is determined showing the typical V-shaped region close to the QCP. Depending on the values of α, we find that also for dimensionalities d⩽2 a finite-temperature critical line, ending in the QCP, exists with asymptotic behaviors and crossovers which can be employed as a useful guide for experimental studies. Moreover, these crossovers are shown to be suitably described in terms of (α,d)-dependent scaling functions and effective critical exponents.