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

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

2008-04-17

arxiv.org/abs/0804.2788v2

Phys. Rev. E 78 (2008) 011110

Physics

Condensed Matter

Disordered Systems and Neural Networks

30 pages

Scientific paper

10.1103/PhysRevE.78.011110

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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