Bond dilution in the 3D Ising model: a Monte Carlo study

TL;DR

This study uses Monte Carlo simulations to analyze how bond dilution affects the critical behavior of the 3D Ising model, revealing the influence of crossover phenomena and confirming the universality class of the disorder fixed point.

Contribution

It provides detailed phase diagrams, critical exponent estimates, and amplitude ratios for the bond-diluted 3D Ising model, highlighting crossover effects and the universality of the disorder fixed point.

Findings

Crossover phenomena significantly affect effective critical exponents.

Amplitude ratios support the universality class of the disorder fixed point.

Critical behavior remains consistent with the site-diluted model.

Abstract

We study by Monte Carlo simulations the influence of bond dilution on the three-dimensional Ising model. This paradigmatic model in its pure version displays a second-order phase transition with a positive specific heat critical exponent $\alpha$. According to the Harris criterion disorder should hence lead to a new fixed point characterized by new critical exponents. We have determined the phase diagram of the diluted model, between the pure model limit and the percolation threshold. For the estimation of critical exponents, we have first performed a finite-size scaling study, where we concentrated on three different dilutions. We emphasize in this work the great influence of the cross-over phenomena between the pure, disorder and percolation fixed points which lead to effective critical exponents dependent on the concentration. In a second set of simulations, the temperature behaviour of physical quantities has been studied in order to characterize the disorder fixed point more accurately. In particular this allowed us to estimate ratios of some critical amplitudes. In accord with previous observations for other models this provides stronger evidence for the existence of the disorder fixed point since the amplitude ratios are more sensitive to the universality class than the critical exponents. Moreover, the question of non-self-averaging at the disorder fixed point is investigated and compared with recent results for the bond-diluted $q=4$ Potts model. Overall our numerical results provide evidence that, as expected on theoretical grounds, the critical behaviour of the bond-diluted model is governed by the same universality class as the site-diluted model.