2004/12/03 by Danuta Makowiec, Makowiec, Danuta
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Cellular Automata and Applications #Cellular automaton #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Condensed matter physics #Discrete mathematics #Enhanced Data Rates for GSM Evolution #FOS: Physical sciences #Ferromagnetism #Graph #Mathematics #Opinion Dynamics and Social Influence #Phase transition #Physics #Random graph #Scale-free network #Spins #Statistical Mechanics (cond-mat.stat-mech) #Statistical physics #Stochastic cellular automaton #Strongly connected component #Theoretical computer science #Topology (electrical circuits) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0412082
arxiv created 2004/12/03 · openalex publication_date 2004/12/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Self-organization to ferromagnetic phase transition in cellular automata of\nspins governed by stochastic majority rule and when topology between spins is\nchanged, is investigated numerically. Three types of edge rewiring are\nconsidered. The algorithm of Watts and Strogatz is applied at each time step to\nestablish a network evolving stochastically (the first network). The preference\nfunctions are defined to amplify the role of strongly connected vertices (the\nsecond network). Demand to preserve graph connectivity provides the third way\nof edge rewiring. Each of these processes yields the different network:\nsmall-world, scattered nodes with one strongly connected component, and\nscale-free network when rewiring is properly adjusted. The stochastic majority\nrule applied to these networks can lead or not to ferromagnetic transition.\nClassical mean-field transition in case of the first and third network is\nobserved. Scale-free ferromagnetic transition can be observed when rewiring is\nproperly adjusted.\n