Critical Properties of Anisotropic Heisenberg Ferromagnet with Spin-One

Combining the two-site cluster approximation with the discretized path-integral representation (DPIR) and Suzuki-Trotter formalism, the critical properties of anisotropic Heisenberg ferromagnet with a crystal field are studied. We find that the tricritical point can appear in the case of negative crystal field. And the exchange anisotropy not only reduces the critical temperature and tricritical point, but also makes re-entrant phenomena instead of the existence of the tricritical point when the exchange anisotropic parameter is larger than a critical value.