Monte Carlo studies of percolation phenomena for a simple cubic lattice |
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| Authors: | Amit Sur Joel L Lebowitz J Marro M H Kalos S Kirkpatrick |
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| Institution: | (1) Belfer Graduate School of Science, Yeshiva University, New York, New York;(2) Present address: Universidad de Barcelona, Departamento de Fisica Teorica, Barcelona, Spain;(3) Courant Institute of Mathematical Sciences, New York University, New York, New York;(4) IBM-T. J. Watson Research Center, Yorktown Heights, New York |
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| Abstract: | The site-percolation problem on a simple cubic lattice is studied by the Monte Carlo method. By combining results for periodic lattices of different sizes through the use of finite-size scaling theory we obtain good estimates forp
c (0.3115±0.0005), (0.41±0.01), (1.6±0.1), and (0.8±0.1). These results are consistent with other studies. The shape of the clusters is also studied. The average  surface area for clusters of sizek is found to be close to its maximal value for the low-concentration region as well as for the critical region. The percentage of particles in clusters of different sizesk is found to have an exponential tail for large values ofk forP <p
c. Forp >p
c there is too much scatter in the data to draw firm conclusions about the size distribution.Work supported in part by USAFOSR Grant #73-2430B and by ERDA #E(11-1)-3077. |
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| Keywords: | Site percolation Monte Carlo method percolation threshold critical exponents finite-size scaling |
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