Spin-1 Blume-Capel model with longitudinal random crystal and transverse magnetic fields: A mean-field approach

The spin-1 Blume-Capel model with transverse Omega and longitudinal external magnetic fields h, in addition to a longitudinal random crystal field D, is studied in the mean-field approximation. It is assumed that the crystal field is either turned on with probability p or turned off with probability 1 - p on the sites of a square lattice. Phase diagrams are then calculated on the reduced temperature crystal field planes for given values of gamma = Omega/J and p at zero h. Thus, the effect of changing gamma and p are illustrated on the phase diagrams in great detail and interesting results are observed.