  We report results of a Wang-Landau study of the random bond square Ising
model with nearest- ($J_{nn}$) and next-nearest-neighbor ($J_{nnn}$)
antiferromagnetic interactions. We consider the case $R=J_{nn}/J_{nnn}=1$ for
which the competitive nature of interactions produces a sublattice ordering
known as superantiferromagnetism and the pure system undergoes a second-order
transition with a positive specific heat exponent $\alpha$. For a particular
disorder strength we study the effects of bond randomness and we find that,
while the critical exponents of the correlation length $\nu$, magnetization
$\beta$, and magnetic susceptibility $\gamma$ increase when compared to the
pure model, the ratios $\beta/\nu$ and $\gamma/\nu$ remain unchanged. Thus, the
disordered system obeys weak universality and hyperscaling similarly to other
two-dimensional disordered systems. However, the specific heat exhibits an
unusually strong saturating behavior which distinguishes the present case of
competing interactions from other two-dimensional random bond systems studied
previously.
