Quantum criticality of a planar Heisenberg ferromagnet in a transverse magnetic field

A one-loop renormalization group treatment is used to investigate the quantum phase transition and the low-temperature critical properties of a planar Heisenberg ferromagnet in a transverse field. The phase diagram, the free energy density and the relevant critical exponents in the influence domain of the quantum critical point are obtained for dimensionalities d⩾2 in the temperature regime where the quantum fluctuations dominate. The (d=2)-criticality is also studied decreasing the temperature with the magnetic field fixed at its critical value. The method of calculation and the peculiarity of the model allow us to work systematically within the region around the critical line where the quantum degrees of freedom govern the low-temperature critical behavior of the model.