  We investigate and contrast, via the Wang-Landau (WL) algorithm, the effects
of quenched bond randomness on the self-averaging properties of two Ising spin
models in 2d. The random bond version of the superantiferromagnetic (SAF)
square model with nearest- and next-nearest-neighbor competing interactions and
the corresponding version of the simple ferromagnetic Ising model are studied.
We find that, the random bond SAF model shows a strong violation of
self-averaging, much stronger than that observed in the case of the random bond
Ising model. Our analysis of the asymptotic scaling behavior of the variance of
the distribution of the sample-dependent pseudocritical temperatures is found
to be consistent with the renormalization group prediction of Aharony and
Harris. Using this alternative approach, we find estimates of the correlation
length exponent $\nu$ in agreement with results obtained from the usual
finite-size scaling (FSS) methodology.
