Purely quadrupolar spin-1 Ising model in a transverse field

A quantum Ising-like spin-1 model characterized by quadrupolar interaction, coupled to an external anisotropic field with both dipole and quadrupole momenta is analyzed. The general phase diagram (including temperature), as well as order parameter, specific heat, and susceptibility are evaluated in the mean-field approximation and exibit a rich structure with transitions of 2° and 1° order and tricritical points. ForT=0 the phase diagram is examined also by a recently formulated improved version of mean-field theory which has the usual mean-field theory as its zero-th order approximation.