Universal dependence on disorder of 2D randomly diluted and random-bond +-J Ising models

TL;DR

This paper investigates the critical behavior of 2D disordered Ising models, demonstrating that disorder induces universal logarithmic corrections at the phase transition, confirmed through analytical renormalization-group analysis and Monte Carlo simulations.

Contribution

It provides a unified analysis of disorder effects on 2D Ising models, showing the universality of logarithmic corrections from both theoretical and numerical perspectives.

Findings

Renormalization-group equations predict universal logarithmic corrections.

Monte Carlo simulations confirm the theoretical predictions.

Disorder acts as a marginally irrelevant perturbation at the 2D Ising fixed point.

Abstract

We consider the two-dimensional randomly site diluted Ising model and the random-bond +-J Ising model (also called Edwards-Anderson model), and study their critical behavior at the paramagnetic-ferromagnetic transition. The critical behavior of thermodynamic quantities can be derived from a set of renormalization-group equations, in which disorder is a marginally irrelevant perturbation at the two-dimensional Ising fixed point. We discuss their solutions, focusing in particular on the universality of the logarithmic corrections arising from the presence of disorder. Then, we present a finite-size scaling analysis of high-statistics Monte Carlo simulations. The numerical results confirm the renormalization-group predictions, and in particular the universality of the logarithmic corrections to the Ising behavior due to quenched dilution.