  This paper considers a model consisting of a kinetic term, Rashba spin-orbit
coupling and short-range Coulomb interaction at zero-temperature. The Coulomb
interaction is decoupled by a mean-field approximation in the spin channel
using field theory methods. The results feature a first-order phase transition
for any finite value of the chemical potential and quantum criticality for
vanishing chemical potential. The Hall conductivity is also computed using Kubo
formula in a mean-field effective Hamiltonian. In the limit of infinite mass
the kinetic term vanishes and all the phase transitions are of second order, in
this case spontaneous symmetry breaking mechanism adds a ferromagnetic metallic
phase to the system and features a zero-temperature quantization of the Hall
conductivity in the insulating one.
