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

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, $ν=0.683(2)$, $η=0.036(1)$, $α=-0.049(6)$, $γ=1.341(4)$, $β=0.354(1)$, $δ=4.792(6)$, and of the leading and next-to-leading correction-to-scaling exponents, $ω=0.33(3)$ and $ω_2=0.82(8)$.