Pike, Robert and Stanley, H. Eugene (1981) Order propagation near the percolation threshold. Journal of Physics A: Mathematical and General, 14 (5). L169-L177. ISSN 0305-4470. http://resolver.caltech.edu/CaltechAUTHORS:20120718-112359479
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A new Monte Carlo method for studying bond percolation clusters is developed and used to identify new critical quantities associated with the percolation threshold. The bonds in each cluster are partitioned into three distinct connectivity classes, 'red' (singly connected backbone bonds), 'blue' (multiply connected backbone bonds) and 'yellow' (non-backbone bonds, often called dangling ends). Among the new cluster properties studied are the mean number of red bonds, a critical quantity diverging at p_c with exponent y_R approximately ≃ 1, and the length of the shortest connected path through the cluster which is critical with exponent y_(min)=1.35 ± 0.02. For all cluster properties studies, the authors also compute averages over only the largest clusters; the corresponding critical exponents are found to be significantly different from those obtained by averaging over clusters of all sizes.
|Additional Information:||© 1981 The Institute of Physics. Received 17 February 1981. Supported in part by grants from ARO and ONR. The authors gratefully acknowledge the assistance of D Hugh Redelmeier in developing the computer program, and helpful interactions with R J Birgeneau, J H Condon, A Coniglio, T D S Duff, F Family, S Kirkpatrick, W Klein, R B Leighton, H Nakanishi, P Pfeuty, S Redner, G R Reich, P J Reynolds, G Shlifer, D Stauffer and S Wolfram. We also thank D S Gaunt for communicating his results to us prior to their publication (Sykes et al 1981).|
|Classification Code:||PACS: 64.60.A-, 02.50.Ng, 64.60.F-. MSC: 82B43, 82B26, 82B80, 82B27|
|Official Citation:||Order propagation near the percolation threshold R Pike and H E Stanley doi:10.1088/0305-4470/14/5/013|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||18 Jul 2012 18:44|
|Last Modified:||23 Aug 2016 10:14|
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