Phase Diagrams of Ising Mixed Integer Spins with Random Anisotropy

The Blume-Capel model with mixed spins S = 1 and S = 2, on a hypercubic lattice, in the presence of random anisotropies, is studied using the mean-field approximation. The disorder is modeled by a two-peak law characterized by the probabilities p and q. The ground state is determined by the aid of the phase diagram in the plane of the two anisotropies (Delta(A) and Delta(B)) for the different values of the probabilities p and q. For T not equal 0 K, the types of possible phase diagrams are given when p and q vary in the plans (Delta(A)/zJ, KBT/zJ) and (Delta(B)/zJ, KBT/zJ). We find the existence of the transition of first, second-order separated by a tricritical point. The locations of tricritical points are determined in the (Delta(A)/zJ, Delta(B)/zJ) plane, this point remains steady in a finite domain of the anisotropy Delta(A)/zJ or Delta(B)/zJ before disappearing. The limited cases of p and q are also treated: when the sublattice of the spins S = 2 is pure, the tricritical behavior disappears. In the inverse case, when the sublattice of the spins S = 1 is pure, the tricritical point persists. This work is completed by a discussion and comparison with other works: Mean-field and Monte Carlo studies of a mixed spin-1 and spin-2 Ising system with different anisotropies, and some other similar models.