1999/07/19 by Giorgio Mazzeo, Reimer Kühn, Reimer Kuehn · 1 citation
Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.60.3823
published as Phys. Rev. E 60, 3823 (1999). · RevTeX file, 15 pages, 6 figures. Accepted for publication in Phys. Rev. E
arxiv created 1999/07/19 · openalex publication_date 1999/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The equilibrium ensemble approach to disordered systems is used to investigate the critical behavior of the two-dimensional Ising model in the presence of quenched random site dilution. The numerical transfer matrix technique in semi-infinite strips of finite width, together with phenomenological renormalization and conformal invariance, is particularly suited to putting the equilibrium ensemble approach to work. A method by which to extract with great precision the critical temperature of the model is proposed and applied. A more systematic finite-size scaling analysis than in previous numerical studies has been performed. A parallel investigation, along the lines of the two main scenarios currently under discussion, namely, the logarithmic corrections scenario (with critical exponents fixed in the Ising universality class) versus the weak universality scenario (critical exponents varying with the degree of disorder), is carried out. In interpreting our data, maximum care is constantly taken to be open to both possibilities. A critical discussion shows that an unambiguous discrimination between the two scenarios is still not possible on the basis of the available finite-size data.