The application of the differential operator method to the Blume-Emery-Griffiths model

Within an effective-field approximation, general expressions for evaluating the second-order phase transition line and the tricritical point of the anisotropic Blume-Emery-Griffiths model are obtained by the use of the differential operator technique. The phase diagrams and the behavior of the tricritical point are investigated numerically for the honeycomb lattice (z = 3) and square lattice (z = 4). We find a new disordered phase which may correspond to the staggered quadrupolar phase predicted in the Monte Carlo simulation, when some conditions are satisfied. The phase diagrams for z = 3 and z = 4 systems exhibit a reentrant behavior for positive values of the uniaxial anisotropy parameter. The change of the tricritical point with the value of the reduced biquadratic parameter is also studied for the system with z = 3.