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

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.

30 pages

References in corpus (3)

• Self-Consistent Scaling Theory for Logarithmic Correction Exponents
• The 3D +-J Ising model at the ferromagnetic transition line
• Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice

Cited by in corpus (5)

• Strong Violation of Critical Phenomena Universality: Wang-Landau Study of the 2d Blume-Capel Model under Bond Randomness
• Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model
• Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions
• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Critical and multicritical behavior of the +- J Ising model in two and three dimensions