Micro mean-field Monte Carlo (MMFMC) method for Heisenberg ferromagnet with arbitrary spin and single-ion anisotropy

We proposed a micro mean-field Monte Carlo (MMFMC) method based on Metropolis single spin flip algorithm to calculate the thermodynamic properties of three-dimensional ferromagnet describerd by Heisenberg model. In MMFMC method, the actions of the neighboring spins on the selected spin is replaced approximately by their expected values multiplied by the exchange interactions between them, thus each spin is in a quantum state obtained by solving single spin Hamitonian in every MC step. The magnetization, internal energy, specific heat, longitudinal and transverse susceptibilities are calculated for SC, BCC and FCC ferromagnets with arbitray spin quantum number and single-ion anisotropy. it is found that the system shows phase transition phenomenon from paramagnetic to ferromagnetic phase with temperature decreasing, and the Curie temperatures obtained are consistent with those obtained by other theories.