Possible crossover of a nonuniversal quantity at the upper critical dimension
We report on a possible crossover of a nonuniversal quantity at the upper critical dimensionality in the field of percolation. Plotting recent estimates for site percolation thresholds of hypercubes in dimension 6 < or =d < or =13 against corresponding predictions from the Galam-Mauger (GM) fo...
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| Published in: | Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 71; no. 3 Pt 2A; p. 036136 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
United States
01-03-2005
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| Online Access: | Get full text |
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| Summary: | We report on a possible crossover of a nonuniversal quantity at the upper critical dimensionality in the field of percolation. Plotting recent estimates for site percolation thresholds of hypercubes in dimension 6 < or =d < or =13 against corresponding predictions from the Galam-Mauger (GM) formula p(c) = p(0) [(d-1) (q-1)](-a) d(b) for percolation thresholds, a significant departure of p(c) is observed for d > or =6 . This result is reminiscent of the crossover undergone by universal quantities in critical phenomena. For bond percolation, evidence of such a crossover of dimensionality would require an improvement of the GM formula to reach a relative error of typically 0.2%, while it is currently at 0.9% for hypercubes. |
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| ISSN: | 1539-3755 1550-2376 |
| DOI: | 10.1103/PhysRevE.71.036136 |