Disorder-averaged Binder ratio in site-diluted Heisenberg models

TL;DR

This paper investigates how the Binder ratio behaves in disordered 3D Heisenberg models, proposing a modified definition and averaging method to account for disorder effects, supported by Monte Carlo simulations.

Contribution

It introduces a modified Binder ratio definition and an averaging procedure tailored for disordered systems, validated through numerical experiments.

Findings

The usual Binder ratio definition needs modification in disordered systems.

A new disorder averaging procedure improves the analysis of Binder ratios.

Numerical results support the proposed modifications.

Abstract

It is demonstrated via a numerical experiment (a Monte Carlo simulation) in the context of three-dimensional site-diluted Heisenberg spin systems that a functional dependence of the Binder ratio ($V_4$) on the order parameter correlation length ($\xi / L$) requires a modification to the usual definition of $V_4$ in disordered systems. An appropriate disorder averaging procedure is proposed.