2014/11/24 by Nikolaos Bastas, Kosmas Kosmidis, Paraskevas Giazitzidis +1 · 10 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Critical exponent #Critical point (mathematics) #Directed percolation #Explosive material #Exponent #Mathematical analysis #Mathematical physics #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Phase transition #Physics #Quantum mechanics #Renormalization group #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.90.062101
published in Physical Review E 90(6), 062101 (American Physical Society) · 6 pages, 5 figures
arxiv created 2014/11/24 · openalex publication_date 2014/12/01 · arxiv updated 2015/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In phase-transition phenomena, the estimation of the critical point is crucial for the calculation of the various critical exponents and the determination of the universality class they belong to. However, this is not an easy task, since a large amount of realizations is needed to eliminate the noise in the data. In this paper, we introduce a novel method for the simultaneous estimation of the critical point p(c) and the critical exponent β/ν, applied for the case of "explosive" bond percolation on two-dimensional square lattices and Erdös-Rényi networks. The results show that with only a few hundred realizations, it is possible to acquire accurate values for these quantities. Guidelines are given at the end for the applicability of the method to other cases as well.