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Article Dans Une Revue The European Physical Journal B: Condensed Matter and Complex Systems Année : 2004

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

Résumé

We study by Monte Carlo simulations the influenceof bond dilution on the three-dimensionalIsing model. This paradigmatic model in its pure version displays a second-order phasetransition with a positive specific heat critical exponent $\alpha$. According to the Harris criteriondisorder should hence lead to a new fixed point characterized by new critical exponents. We havedetermined 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, disorderand 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 inorder 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 questionof non-self-averaging at the disorder fixed point isinvestigated 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.
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Dates et versions

hal-00001186 , version 1 (24-02-2004)

Identifiants

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Pierre-Emmanuel Berche, Christophe Chatelain, Bertrand Berche, Wolfhard Janke. Bond dilution in the 3D Ising model: a Monte Carlo study. The European Physical Journal B: Condensed Matter and Complex Systems, 2004, 38, pp.463-474. ⟨10.1140/epjb/e2004-00141-x⟩. ⟨hal-00001186⟩
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