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 ν=0.688(13) is found which is well above the result ν=0.629(4) for the pure model and above the exact lower bound of ν=2/3, and the relative width of the asymptotic regime is definitely larger than 3×${10}^{\mathrm{-}4}$. 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×${10}^{\mathrm{-}4}$, and that it can hardly be explored by experiments or computer simulations.

• Received 1 March 1990

DOI:https://doi.org/10.1103/PhysRevB.41.11709