Quenched bond randomness in marginal and non-marginal Ising spin models in 2D

TL;DR

This study uses entropic sampling to analyze how quenched bond randomness affects the critical behavior of 2D Ising models, revealing different universality classes and confirming logarithmic corrections in the random Ising case.

Contribution

It provides a detailed finite-size scaling analysis of two 2D Ising models with quenched bond randomness, highlighting their universality properties and confirming theoretical predictions.

Findings

Random SAF model obeys weak universality and hyperscaling.

Specific heat saturates due to competing interactions.

Data favors logarithmic corrections in the random Ising model.

Abstract

We investigate and contrast, via entropic sampling based on the Wang-Landau algorithm, the effects of quenched bond randomness on the critical behavior of two Ising spin models in 2D. The random bond version of the superantiferromagnetic (SAF) square model with nearest- and next-nearest-neighbor competing interactions and the corresponding version of the simple Ising model are studied and their general universality aspects are inspected by a detailed finite-size scaling (FSS) analysis. We find that, the random bond SAF model obeys weak universality, hyperscaling, and exhibits a strong saturating behavior of the specific heat due to the competing nature of interactions. On the other hand, for the random Ising model we encounter some difficulties for a definite discrimination between the two well-known scenarios of the logarithmic corrections versus the weak universality. Yet, a careful FSS analysis of our data favors the field-theoretically predicted logarithmic corrections.