Order propagation near the percolation threshold
- Creators
- Pike, Robert
- Stanley, H. Eugene
Abstract
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).Additional details
- Eprint ID
- 32552
- Resolver ID
- CaltechAUTHORS:20120718-112359479
- Army Research Office (ARO)
- Office of Naval Research (ONR)
- Created
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2012-07-18Created from EPrint's datestamp field
- Updated
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2022-07-12Created from EPrint's last_modified field