Phase diagram of the spin-1 anisotropic Heisenberg model with a single-ion anisotropy

The spin-1 anisotropic Heisenberg model with a single-ion anisotropy is studied using the Oguchi's pair approximation. Although the theory is developed for lattices with general coordination number, we treat in detail the three-dimensional lattice with the lowest coordination number, i.e. diamond lattice, where the critical and tricritical behavior of the system is analyzed as a function of both the single-ion anisotropy and exchange anisotropy.