Phase Transition in Long-Range Percolation on Bipartite Hierarchical Lattices
We propose a family of bipartite hierarchical lattice of order N governed by a pair of parameters and . We study long-range percolation on the bipartite hierarchical lattice where any edge (running between vertices of unlike bipartition sets) of length k is present with probability , independently...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2013/172393 |
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| Summary: | We propose a family of bipartite hierarchical lattice of order N governed by a pair of parameters and . We study long-range percolation on the bipartite hierarchical lattice where any edge (running between vertices of unlike bipartition sets) of length k is present with probability , independently of all other edges. The parameter is the percolation parameter, while describes the long-range nature of the model. The model exhibits a nontrivial phase transition in the sense that a critical value if and only if and . Moreover, the infinite component is unique when . |
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| ISSN: | 1537-744X |