PERSISTENCE IN THE ZERO-TEMPERATURE DYNAMICS OF THEQ-STATES POTTS MODEL ON UNDIRECTED-DIRECTED BARABÁSI–ALBERT NETWORKS AND ERDÖS–RÉNYI RANDOM GRAPHS

F. P. Fernandes and F. W. S. Lima ()
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F. P. Fernandes: Departamento de Física, Universidade Federal do Piauí, 64049-550 Teresina, PI, Brazil
F. W. S. Lima: Departamento de Física, Universidade Federal do Piauí, 64049-550 Teresina, PI, Brazil

International Journal of Modern Physics C (IJMPC), 2008, vol. 19, issue 12, 1777-1785

Abstract: The zero-temperature Glauber dynamics is used to investigate the persistence probabilityP(t)in the Potts model withQ = 3, 4, 5, 7, 9, 12, 24, 64, 128, 256, 512, 1024, 4096, 16 384, …, 230states ondirectedandundirectedBarabási–Albert networks and Erdös–Rényi (ER) random graphs. In this model, it is found thatP(t)decays exponentially to zero in short times fordirectedandundirectedER random graphs. FordirectedandundirectedBA networks, in contrast it decays exponentially to a constant value for long times, i.e.,P(∞)is different from zero for allQvalues (here studied) fromQ = 3, 4, 5, …, 230; this shows "blocking" for all theseQvalues. Except that forQ = 230in theundirectedcaseP(t)tends exponentially to zero; this could be just a finite-size effect since in the other "blocking" cases you may have only a few unchanged spins.

Keywords: Monte Carlo simulation; spins; networks; Potts (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S0129183108013345

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