We study the Glauber dynamics at zero temperature of spins placed on the vertices of an uncorrelated network with a power law degree distribution. Application of mean-field theory yields as the main prediction that for symmetric disordered initial conditions the mean time for reaching full order is finite or diverges as a logarithm of the system size N , depending on the exponent of the degree distribution. Extensive numerical simulations contradict these results and clearly show that the mean-field assumption is not appropriate for describing this problem.(more)
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%0 Journal Article
%1 Castellano2006Zero
%A Castellano, Claudio
%A Pastor-Satorras, Romualdo
%D 2006
%I Institute of Physics Publishing
%J Journal of Statistical Mechanics: Theory and Experiment
%K ising-glauber-model, mean-field, networks
%N 05
%P P05001+
%R 10.1088/1742-5468/2006/05/p05001
%T Zero temperature Glauber dynamics on complex networks
%U http://dx.doi.org/10.1088/1742-5468/2006/05/p05001
%V 2006
%X We study the Glauber dynamics at zero temperature of spins placed on the vertices of an uncorrelated network with a power law degree distribution. Application of mean-field theory yields as the main prediction that for symmetric disordered initial conditions the mean time for reaching full order is finite or diverges as a logarithm of the system size N , depending on the exponent of the degree distribution. Extensive numerical simulations contradict these results and clearly show that the mean-field assumption is not appropriate for describing this problem.
@article{Castellano2006Zero,
abstract = {{We study the Glauber dynamics at zero temperature of spins placed on the vertices of an uncorrelated network with a power law degree distribution. Application of mean-field theory yields as the main prediction that for symmetric disordered initial conditions the mean time for reaching full order is finite or diverges as a logarithm of the system size N , depending on the exponent of the degree distribution. Extensive numerical simulations contradict these results and clearly show that the mean-field assumption is not appropriate for describing this problem.}},
added-at = {2019-06-10T14:53:09.000+0200},
archiveprefix = {arXiv},
author = {Castellano, Claudio and Pastor-Satorras, Romualdo},
biburl = {https://www.bibsonomy.org/bibtex/288033680e9f2696093260c76b3bb5244/nonancourt},
citeulike-article-id = {612210},
citeulike-linkout-0 = {http://arxiv.org/abs/cond-mat/0602315},
citeulike-linkout-1 = {http://arxiv.org/pdf/cond-mat/0602315},
citeulike-linkout-2 = {http://dx.doi.org/10.1088/1742-5468/2006/05/p05001},
citeulike-linkout-3 = {http://iopscience.iop.org/1742-5468/2006/05/P05001},
citeulike-linkout-4 = {http://adsabs.harvard.edu/cgi-bin/nph-bib\_query?bibcode=2006JSMTE..05..001C},
day = 03,
doi = {10.1088/1742-5468/2006/05/p05001},
eprint = {cond-mat/0602315},
interhash = {6cf2f4bf901cd3281413dc8e740b51c5},
intrahash = {88033680e9f2696093260c76b3bb5244},
issn = {1742-5468},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
keywords = {ising-glauber-model, mean-field, networks},
month = may,
number = 05,
pages = {P05001+},
posted-at = {2012-09-06 22:53:40},
priority = {2},
publisher = {Institute of Physics Publishing},
timestamp = {2019-06-10T14:53:09.000+0200},
title = {{Zero temperature Glauber dynamics on complex networks}},
url = {http://dx.doi.org/10.1088/1742-5468/2006/05/p05001},
volume = 2006,
year = 2006
}