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arXiv · 0804.2788

Universal dependence on disorder of 2D randomly diluted and random-bond +-J Ising models

M. Hasenbusch·F. Parisen Toldin·A. Pelissetto·E. Vicari
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Abstract

We consider the two-dimensional randomly site diluted Ising model and the random-bond +-J Ising model (also called Edwards-Anderson model), and study their critical behavior at the paramagnetic-ferromagnetic transition. The critical behavior of thermodynamic quantities can be derived from a set of renormalization-group equations, in which disorder is a marginally irrelevant perturbation at the two-dimensional Ising fixed point. We discuss their solutions, focusing in particular on the universality of the logarithmic corrections arising from the presence of disorder. Then, we present a finite-size scaling analysis of high-statistics Monte Carlo simulations. The numerical results confirm the renormalization-group predictions, and in particular the universality of the logarithmic corrections to the Ising behavior due to quenched dilution.

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M. Hasenbusch, F. Parisen Toldin, A. Pelissetto, E. Vicari. 2008-07-18. Universal dependence on disorder of 2D randomly diluted and random-bond +-J Ising models. https://doi.org/10.1103/physreve.78.011110

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