Scaling analysis of the site-diluted Ising model in two dimensions

2008/07/31 by Ralph Kenna, R. Kenna, J. J. Ruiz-Lorenzo
Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.78.031134

published as Phys. Rev. E 78 (2008) 031134 · 15 pages, 3 figures. Published version

openalex publication_date 2008/09/29 · arxiv created 2008/09/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A combination of recent numerical and theoretical advances are applied to analyze the scaling behavior 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.

Citations

• Correlation-length–exponent relation for the two-dimensional random Ising model
• Renormalization group theory: Its basis and formulation in statistical physics
• Critical behavior of the two-dimensional spin-diluted Ising model via the equilibrium ensemble approach
• Fermionic structure of two-dimensional Ising model with quenched site dilution
• Critical behaviour of the phase transition in the 2D Ising Model with impurities