External surface of site percolation clusters in three dimensions
Q Cao; P Wong; Q Cao; Dept. of Phys. & Astron., Massachusetts Univ., Amherst, MA, USA; P Wong; Dept. of Phys. & Astron., Massachusetts Univ., Amherst, MA, USA
Журнал:
Journal of Physics A: Mathematical and General
Дата:
1992-01-21
Аннотация:
The authors study the external surface of site-percolation clusters in three dimensions by Monte Carlo simulations on a simple cubic lattice at p=p<sub>c</sub>=0.3117. Their results show that for all cluster sizes, s, more than 99.8% of the occupied sites are on the external surface. The number of unoccupied boundary sites t is found to obey t/s=(1-p<sub>c</sub>)/p<sub>c</sub>+As<sup>- psi </sup> with psi =0.54=1- sigma , in agreement with the prediction of a scaling argument. The same argument also predicts psi =0.60 in two dimensions and it is confirmed. The relevance of these results to dynamical percolation growth models is discussed.
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