Universality class of 3D site-diluted and bond-diluted Ising systems

TL;DR

This study uses finite-size scaling and improved Hamiltonians in high-statistics Monte Carlo simulations to accurately determine the universal critical behavior of 3D site- and bond-diluted Ising models, confirming they share the same universality class.

Contribution

The paper demonstrates that improved Hamiltonians and observables effectively control scaling corrections, enabling precise determination of the universality class and critical exponents of diluted 3D Ising systems.

Findings

Phase transitions in the models belong to the same universality class.

Accurate critical exponents are estimated: ν=0.683(2), η=0.036(1).

Leading correction-to-scaling exponent ω=0.33(3).

Abstract

We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behavior of these systems is affected by slowly-decaying scaling corrections which make the accurate determination of their universal asymptotic behavior quite hard, requiring an effective control of the scaling corrections. For this purpose we exploit improved Hamiltonians, for which the leading scaling corrections are suppressed for any thermodynamic quantity, and improved observables, for which the leading scaling corrections are suppressed for any model belonging to the same universality class. The results of the finite-size scaling analysis provide strong numerical evidence that phase transitions in three-dimensional randomly site-diluted and bond-diluted Ising models belong to the same randomly dilute Ising universality class. We obtain accurate estimates of the critical exponents, $\nu=0.683(2)$, $\eta=0.036(1)$, $\alpha=-0.049(6)$, $\gamma=1.341(4)$, $\beta=0.354(1)$, $\delta=4.792(6)$, and of the leading and next-to-leading correction-to-scaling exponents, $\omega=0.33(3)$ and $\omega_2=0.82(8)$.