Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions

Abstract

A combination of recent numerical and theoretical advances are applied to analyze the scaling behaviour of the site-diluted Ising model in two dimensions, paying special attention to the implications for multiplicative logarithmic corrections. The analysis focuses primarily on the odd sector of the model (i.e., that associated with magnetic exponents), and in particular on its Lee-Yang zeros, which are determined to high accuracy. Scaling relations are used to connect to the even (thermal) sector, and a first analysis of the density of zeros yields information on the specific heat and its corrections. The analysis is fully supportive of the strong scaling hypothesis and of the scaling relations for logarithmic corrections.

15 pages, 3 figures. Published version

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• Quenched bond randomness in marginal and non-marginal Ising spin models in 2D
• Ising-like critical behavior of vortex lattices in an active fluid
• Critical behavior of the pure and random-bond two-dimensional triangular Ising ferromagnet
• Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field
• Spin Glass in the Bond-Diluted J1-J2 Ising Model on the Square Lattice
• Super slowing down in the bond-diluted Ising model
• Two-dimensional Ising model on random lattices with constant coordination number
• Observation of mixed anisotropy in the critical susceptibility of an ultrathin magnetic film
• Self-averaging in the random 2D Ising ferromagnet
• Stripe order, impurities, and symmetry breaking in a diluted frustrated magnet
• The Site-Diluted Ising Model in Four Dimension
• Dynamic approach to finite-temperature magnetic phase transitions in the extended J1- J2 model with vacancy order
• Corrections to scaling in the dynamic approach to the phase transition with quenched disorder
• Fermions and Disorder in Ising and Related Models in Two Dimensions
• Emerging critical behavior at a first-order phase transition rounded by disorder
• Numerical study of the overlap Lee-Yang singularities in the three-dimensional Edwards-Anderson model
• Emergent universal critical behavior of the 2D $N$-color Ashkin-Teller model in the presence of correlated disorder
• Lack of self-averaging of the critical internal energy in a weakly-disordered Baxter model