Self-Averaging in the Three Dimensional Site Diluted Heisenberg Model at the critical point

TL;DR

This paper investigates the self-averaging behavior of the three-dimensional site diluted Heisenberg model at criticality, confirming theoretical predictions with numerical results and emphasizing the importance of scaling corrections.

Contribution

The study provides numerical evidence that self-averaging properties align with Harris criterion predictions when scaling corrections are included.

Findings

Self-averaging susceptibility at criticality confirmed with scaling corrections.

Critical exponents match those of the pure model, supporting universality.

Disorder effects are negligible when scaling corrections are properly considered.

Abstract

We study the self-averaging properties of the three dimensional site diluted Heisenberg model. The Harris criterion \cite{critharris} states that disorder is irrelevant since the specific heat critical exponent of the pure model is negative. According with some analytical approaches \cite{harris}, this implies that the susceptibility should be self-averaging at the critical temperature ($R_\chi=0$). We have checked this theoretical prediction for a large range of dilution (including strong dilution) at critically and we have found that the introduction of scaling corrections is crucial in order to obtain self-averageness in this model. Finally we have computed critical exponents and cumulants which compare very well with those of the pure model supporting the Universality predicted by the Harris criterion.