The Monte Carlo renormalization-group approach is applied to investigate the critical behavior of the simple-cubic Ising model diluted randomly with nonmagnetic atoms of concentration x. For x=0.2 a value of \ensuremath{\nu}=0.688(13) is found which is well above the result \ensuremath{\nu}=0.629(4) for the pure model and above the exact lower bound of \ensuremath{\nu}=2/3, and the relative width of the asymptotic regime is definitely larger than 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$. For x=0.1 the obtained value is below the exact lower bound, possibly indicating that the asymptotic critical regime has not been penetrated, that this regime has a width smaller than 1.3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$, and that it can hardly be explored by experiments or computer simulations.
We study the diluted site-bond-correlated (SBC) Ising model within the scheme of the mean-field renormalization group. The SBC Ising model has been proposed to describe the phase diagram for
KNip${\mathrm{Mg}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$
F3. One treats the square (Z=4) and simple cubic (Z=6) lattices by using two different exchange interactions (denoted by models A and B). In the present paper, the phase diagram for some values of the correlation parameter \ensuremath{\alpha}, which range from zero to unity, is studied. We obtain two critical concentrations
pc(\ensuremath{\alpha}=0) and
pc(\ensuremath{\alpha}\ensuremath{\ne}0) in agreement with results from Monte Carlo methods. In addition, an interesting universal relation between the initial slope ${\mathrm{\ensuremath{\Delta}}}^{(\mathrm{\ensuremath{\mu}})}$(\ensuremath{\alpha}=1) and ${\mathrm{\ensuremath{\Delta}}}^{(\mathrm{\ensuremath{\mu}})}$(\ensuremath{\alpha}=0) is obtained (\ensuremath{\mu} denotes model A or B). From this relation, we can estimate the possible exact values to the initial slope on the completely correlated case. Our approach is valid for lattices with any coordination number Z.