Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet

TL;DR

This study examines how quenched bond randomness influences the critical behavior of the two-dimensional triangular Ising ferromagnet, confirming the presence of logarithmic corrections predicted by field theory through finite-size scaling analysis.

Contribution

It provides a detailed finite-size scaling analysis of both pure and disordered models, supporting the logarithmic corrections scenario over weak universality.

Findings

Logarithmic corrections dominate the disordered model's critical behavior.

Finite-size scaling confirms the field-theoretic predictions.

Sample-to-sample fluctuations scale consistently with the logarithmic correction scenario.

Abstract

We investigate the effects of quenched bond randomness on the critical properties of the two-dimensional ferromagnetic Ising model embedded in a triangular lattice. The system is studied in both the pure and disordered versions by the same efficient two-stage Wang-Landau method. In the first part of our study we present the finite-size scaling behavior of the pure model, for which we calculate the critical amplitude of the specific heat's logarithmic expansion. For the disordered system, the numerical data and the relevant detailed finite-size scaling analysis along the lines of the two well-known scenarios - logarithmic corrections versus weak universality - strongly support the field-theoretically predicted scenario of logarithmic corrections. A particular interest is paid to the sample-to-sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality.