Shortest-path fractal dimension for percolation in two and three dimensions

Zongzheng Zhou, Ji Yang, Youjin Deng, Robert M. Ziff

Research output: Contribution to journalArticleResearchpeer-review

27 Citations (Scopus)


We carry out a high-precision Monte Carlo study of the shortest-path fractal dimension dmin for percolation in two and three dimensions, using the Leath-Alexandrowicz method which grows a cluster from an active seed site. A variety of quantities are sampled as a function of the chemical distance, including the number of activated sites, a measure of the radius, and the survival probability. By finite-size scaling, we determine d min=1.13077(2) and 1.3756(6) in two and three dimensions, respectively. The result in two dimensions rules out the recently conjectured value dmin=217/192.
Original languageEnglish
Article number061101
Pages (from-to)1-5
Number of pages5
JournalPhysical Review E
Issue number6
Publication statusPublished - 4 Dec 2012
Externally publishedYes

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