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

TL;DR

This study uses Wang-Landau simulations to analyze how bond randomness affects the critical behavior of a 2D square Ising model with competing nearest and next-nearest neighbor antiferromagnetic interactions, revealing weak universality and unique specific heat behavior.

Contribution

It provides the first detailed analysis of the random bond square Ising model with competing interactions using Wang-Landau sampling, highlighting weak universality and distinctive thermodynamic features.

Findings

Critical exponents increase with disorder but ratios remain constant.

The system exhibits weak universality and hyperscaling.

Specific heat shows strong saturation behavior.

Abstract

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.