Scaling and self-averaging in the three-dimensional random-field Ising model

TL;DR

This study uses extensive Monte Carlo simulations to analyze the critical behavior of the 3D random-field Ising model under strong disorder, confirming the two-exponent scaling scenario and highlighting significant self-averaging violations.

Contribution

It provides numerical evidence supporting the two-exponent scaling scenario and demonstrates the strong violation of self-averaging in the ordered phase of the model.

Findings

Supports the two-exponent scaling scenario with $ar{ ext{eta}}=2 ext{eta}$

Shows strong violation of self-averaging in the ordered phase

Uses finite-size measures and noise-to-signal ratios for analysis

Abstract

We investigate, by means of extensive Monte Carlo simulations, the magnetic critical behavior of the three-dimensional bimodal random-field Ising model at the strong disorder regime. We present results in favor of the two-exponent scaling scenario, $\bar{\eta}=2\eta$, where $\eta$ and $\bar{\eta}$ are the critical exponents describing the power-law decay of the connected and disconnected correlation functions and we illustrate, using various finite-size measures and properly defined noise to signal ratios, the strong violation of self-averaging of the model in the ordered phase.