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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| Format: | Article |
| Language: | English |
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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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| author | Yilun Shang |
| author_facet | Yilun Shang |
| author_sort | Yilun Shang |
| collection | DOAJ |
| description | 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 . |
| format | Article |
| id | doaj-art-783a5c1ecb304b1c95768e5c87518397 |
| institution | Kabale University |
| issn | 1537-744X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-783a5c1ecb304b1c95768e5c875183972025-02-03T01:20:49ZengWileyThe Scientific World Journal1537-744X2013-01-01201310.1155/2013/172393172393Phase Transition in Long-Range Percolation on Bipartite Hierarchical LatticesYilun Shang0Singapore University of Technology and Design, 20 Dover Drive, 138682, SingaporeWe 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 .http://dx.doi.org/10.1155/2013/172393 |
| spellingShingle | Yilun Shang Phase Transition in Long-Range Percolation on Bipartite Hierarchical Lattices The Scientific World Journal |
| title | Phase Transition in Long-Range Percolation on Bipartite Hierarchical Lattices |
| title_full | Phase Transition in Long-Range Percolation on Bipartite Hierarchical Lattices |
| title_fullStr | Phase Transition in Long-Range Percolation on Bipartite Hierarchical Lattices |
| title_full_unstemmed | Phase Transition in Long-Range Percolation on Bipartite Hierarchical Lattices |
| title_short | Phase Transition in Long-Range Percolation on Bipartite Hierarchical Lattices |
| title_sort | phase transition in long range percolation on bipartite hierarchical lattices |
| url | http://dx.doi.org/10.1155/2013/172393 |
| work_keys_str_mv | AT yilunshang phasetransitioninlongrangepercolationonbipartitehierarchicallattices |