  We report on large-scale Wang-Landau Monte Carlo simulations of the critical
behavior of two spin models in two- (2d) and three-dimensions (3d), namely the
2d random-bond Ising model and the pure 3d Blume-Capel model at zero
crystal-field coupling. The numerical data we obtain and the relevant
finite-size scaling analysis provide clear answers regarding the universality
aspects of both models. In particular, for the random-bond case of the 2d Ising
model the theoretically predicted strong universality's hypothesis is verified,
whereas for the second-order regime of the Blume-Capel model, the expected
$d=3$ Ising universality is verified. Our study is facilitated by the combined
use of the Wang-Landau algorithm and the critical energy subspace scheme,
indicating that the proposed scheme is able to provide accurate results on the
critical behavior of complex spin systems.
