Properties of spin- transverse Ising model with anisotropic crystal field on a honeycomb lattice

The properties of spin- transverse Ising model with the anisotropic crystal field interaction are studied by using the effective-field theory with correlations based on both the approximated Van der Waerden identity and the differential operator technique. The longitudinal and transverse magnetizations and the internal energy and specific heat are obtained numerically for the honeycomb lattice (z=3). We find a number of interesting phenomena in these quantities, due to the fluctuation of anisotropic crystal field interaction and the transverse field.