Isotropic and anisotropic quantum Heisenberg models under bond randomness: An effective-field theory study

We study phase transition properties of the isotropic and anisotropic quantum Heisenberg models for the three dimensional simple cubic lattice under bond randomness. Effects of hamiltonian parameters on the phase diagrams and also magnetization profiles have been discussed. After a detailed analysis, our numerical findings indicate that present system shows interesting magnetic behaviors. For example, when the anisotropy parameters are selected to be relatively small, the system exhibits second order phase transition. However, as the anisotropy parameters exceed a characteristic value, first order phase transition occurs between ordered and disordered phases. We note that this multicritical behavior sensitively depends on the selected values of the bond randomness as well as anisotropy parameters.