The phase diagram of modified random-bond Ising model has been investigated. The model is based on random-bond Ising model in which the distribution of magnetic interaction is Gaussian rather than the uniform distribution. The center of the distribution is positive so that most of the interactions are ferromagnetic. However the width of the distribution can be varied. The increasing of the width (J) induces disorder to this system. It is expected that when the tail of the distribution reaches the negative interaction region, the system at low temperature shows the cross over between ferromagnetic phase and spin glass phase. By using magnetization and spin glass magnetization, three ordered phases appear in the J-T phase diagram: (1) the ferromagnetic (FM) phase; (2) the spin glass (SG) phase; (3) the paramagnetic (PM) phase. At very high temperature the system is in paramagnetic phase. At low temperature and small distribution the system is in ferromagnetic phase. The cross over between ferromagnetic phase and spin glass phase is visible as the width of the interaction distribution is increase at low temperature. The critical temperature has been obtained by using Binder cumulant of spin glass magnetization.
An Ising model including field randomness and $\ifmmode\pm\else\textpm\fi{}J$ bond randomness is studied by renormalization-group theory in spatial dimensions
d=2 and 3. In
d=3, with field randomness but no $\ifmmode\pm\else\textpm\fi{}J$ randomness, ferromagnetic and paramagnetic phases occur with no intervening spin-glass phase. Also in
d=3, at sufficient $\ifmmode\pm\else\textpm\fi{}J$ randomness, a spin-glass phase occurs, but is replaced by the paramagnetic phase for any nonzero random field, also implying its disappearance for any nonzero uniform field. In
d=2, no ferromagnetic phase under random fields and no spin-glass phase occur. Global phase diagrams uniting the random-field and spin-glass problems are evaluated. The strong violation of critical phenomena universality, previously found adjoining random-bond tricriticality in
d=3, is seen here in
d=2.We study the ±J three-dimensional (3D) Ising model with a spatially uniaxial anisotropic bond randomness on the simple cubic lattice. The ±J random exchange is applied on the xy planes, whereas, in the z direction, only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied at the ferromagnetic-paramagnetic transition line using parallel tempering and a convenient concentration of antiferromagnetic bonds (p(z)=0;p(xy)=0.176). The numerical data clearly point out a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3D random Ising model. The smooth finite-size behavior of the effective exponents, describing the peaks of the logarithmic derivatives of the order parameter, provides an accurate estimate of the critical exponent 1/ν=1.463(3), and a collapse analysis of magnetization data gives an estimate of β/ν=0.516(7). These results are in agreement with previous papers and, in particular, with those of the isotropic ±J three-dimensional Ising model at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.