Zhou Z, Yang J, Deng Y, Ziff RM. Shortest-path fractal dimension for percolation in two and three dimensions.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012;
86:061101. [PMID:
23367887 DOI:
10.1103/physreve.86.061101]
[Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2012] [Indexed: 05/28/2023]
Abstract
We carry out a high-precision Monte Carlo study of the shortest-path fractal dimension d(min) 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 d(min)=217/192 [Deng et al., Phys. Rev. E 81, 020102(R) (2010)].
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