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

We report results from a Wang–Landau study of the random bond square Ising model with nearest-neighbor (Jnn) and next-nearest-neighbor (Jnnn) antiferromagnetic interactions. We consider the case R = Jnn/Jnnn = 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 α. For a particular disorder strength we study the effects of bond randomness and we find that, while the critical exponents of the correlation length ν, magnetization β, and magnetic susceptibility γ increase as compared to the pure model, the ratios β/ν and γ/ν 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.