2010/12/19 by David R. de Souza, David R. Souza, Tânia Tomé +1 · 27 citations
Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Criticality #Electrical resistivity and conductivity #Geometry #Invariant (physics) #Mathematical physics #Mathematics #Moment (physics) #Percolation (cognitive psychology) #Percolation theory #Percolation threshold #Physics #Quantum mechanics #Scale invariance #Scaling #Second moment of area #Square (algebra) #Square lattice #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Topology (electrical circuits) #cond-mat.dis-nn
paper · pdf · doi:10.1088/1742-5468/2011/03/p03006
published in Journal of Statistical Mechanics Theory and Experiment 2011(03), P03006 (Institute of Physics)
arxiv created 2010/12/19 · openalex publication_date 2011/03/04 · arxiv updated 2011/03/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
The critical behavior of the stochastic susceptible–infected–recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP , equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P , is shown to have, for a square system, a universal value 1.0167(1) that is the same for site and bond percolation, confirming further that the SIR model is also in the percolation class.