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We report results of a Wang-Landau study of the random bond square Isingmodel with nearest- ($J_{nn}$) and next-nearest-neighbor ($J_{nnn}$)antiferromagnetic interactions. We consider the case $R=J_{nn}/J_{nnn}=1$ forwhich the competitive nature of interactions produces a sublattice orderingknown as superantiferromagnetism and the pure system undergoes a second-ordertransition with a positive specific heat exponent $\alpha$. For a particulardisorder 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 thepure model, the ratios $\beta/\nu$ and $\gamma/\nu$ remain unchanged. Thus, thedisordered system obeys weak universality and hyperscaling similarly to othertwo-dimensional disordered systems. However, the specific heat exhibits anunusually strong saturating behavior which distinguishes the present case ofcompeting interactions from other two-dimensional random bond systems studiedpreviously.

Wang-Landau study of the random bond square Ising model with nearest- and next-nearest-neighbor interactions