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 $ u$, magnetization $beta$, and magnetic susceptibility $gamma$ increase when compared to the pure model, the ratios $beta/ u$ and $gamma/ u$ 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.
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