On weak vs. strong universality in the two-dimensional random-bond Ising ferromagnet

TL;DR

This paper investigates universality in two-dimensional disordered Ising models, showing that incorporating logarithmic corrections aligns disordered systems with pure system behavior, challenging the weak-universality scenario.

Contribution

It proposes an ansatz for size-dependent logarithmic corrections to correlation lengths, demonstrating that pure system universality is recovered in disordered systems when these are included.

Findings

Pure system behavior with ν=1 is recovered with corrections.

Logarithmic corrections explain deviations from pure behavior.

Weak-universality scenario is discarded based on data.

Abstract

We address the issue of universality in two-dimensional disordered Ising systems, by considering long, finite-width strips of ferromagnetic Ising spins with randomly distributed couplings. We calculate the free energy and spin-spin correlation functions (from which averaged correlation lengths, $\xi^{ave}$, are computed) by transfer-matrix methods. An {\it ansatz} for the size-dependence of logarithmic corrections to $\xi^{ave}$ is proposed. Data for both random-bond and site-diluted systems show that pure system behaviour (with $\nu=1$) is recovered if these corrections are incorporated, discarding the weak--universality scenario.