Two-dimensional Dilute Ising Models: Defect Lines and the Universality of the Critical Exponent \nu

TL;DR

This study uses Monte Carlo simulations to analyze defect lines in two-dimensional random Ising models, revealing non-universal local critical behavior at defects but universal bulk critical exponent =1.

Contribution

It provides new evidence that the bulk correlation length exponent  remains constant at 1, regardless of bond dilution, despite local non-universal behavior.

Findings

Defect magnetization critical exponent varies with defect strength.

Bulk correlation length exponent  is independent of dilution.

Local critical behavior is non-universal at defect lines.

Abstract

We consider two-dimensional Ising models with randomly distributed ferromagnetic bonds and study the local critical behavior at defect lines by extensive Monte Carlo simulations. Both for ladder and chain type defects, non-universal critical behavior is observed: the critical exponent of the defect magnetization is found to be a continuous function of the strength of the defect coupling. Analyzing corresponding stability conditions, we obtain new evidence that the critical exponent $\nu$ of the bulk correlation length of the random Ising model does not depend on dilution, i.e. $\nu=1$.