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Site percolation and random walks on d-dimensional Kagome lattices | | Steven C. van der Marck
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13 Dec 1997 | | Journal: | J. Phys. A: Math. Gen. 31 (1998) 3449--3460. | | Subject: | Statistical Mechanics | cond-mat.stat-mech | | Affiliation: | SIEP Research and Technical Services | | Abstract: | The site percolation problem is studied on d-dimensional generalisations of the Kagome’ lattice. These lattices are isotropic and have the same coordination number q as the hyper-cubic lattices in d dimensions, namely q=2d. The site percolation thresholds are calculated numerically for d= 3, 4, 5, and 6. The scaling of these thresholds as a function of dimension d, or alternatively q, is different than for hypercubic lattices: p_c ~ 2/q instead of p_c ~ 1/(q-1). The latter is the Bethe approximation, which is usually assumed to hold for all lattices in high dimensions. A series expansion is calculated, in order to understand the different behaviour of the Kagome’ lattice. The return probability of a random walker on these lattices is also shown to scale as 2/q. For bond percolation on d-dimensional diamond lattices these results imply p_c ~ 1/(q-1). | | Source: | arXiv, cond-mat/9801112 | | Services: | Forum | Review | PDF | Favorites | |
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