2000/08/08 by Yamir Moreno, Y. Moreno, Javier B. Gómez +2 · 98 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Approx #Branching (polymer chemistry) #Bundle #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Computer science #Condensed matter physics #Critical exponent #Exponent #Magnetic field #Magnetization #Materials science #Mathematics #Order (exchange) #Phase transition #Physics #Probabilistic logic #Quantum mechanics #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.85.2865
published in Physical Review Letters 85(14), 2865-2868 (American Physical Society) · 5 pages, 5 figures, APS style, submitted for publication
arxiv created 2000/08/08 · openalex publication_date 2000/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using the global fiber bundle model as a tractable scheme of progressive fracture in heterogeneous materials, we define the branching ratio in avalanches as a suitable order parameter to clarify the order of the phase transition occurring at the collapse of the system. The model is analyzed using a probabilistic approach suited to smooth fluctuations. The branching ratio shows a behavior analogous to the magnetization in known magnetic systems with second-order phase transitions. We obtain a universal critical exponent beta approximately = 0.5 independent of the probability distribution used to assign the strengths of individual fibers.