Inequality for the infinite-cluster density in Bernoulli percolation
Journal Article
·
· Phys. Rev. Lett.; (United States)
Under a certain assumption (which is satisfied whenever there is a dense infinite cluster in the half-space), we prove a differential inequality for the infinite-cluster density, P/sub infinity/(p), in Bernoulli percolation. The principal implication of this result is that if P/sub infinity/(p) vanishes with critical exponent ..beta.., then ..beta.. obeys the mean-field bound ..beta..< or =1. As a corollary, we also derive an inequality relating the backbone density, the truncated susceptibility, and the infinite-cluster density.
- Research Organization:
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853
- DOE Contract Number:
- AC02-83ER13044
- OSTI ID:
- 5920710
- Journal Information:
- Phys. Rev. Lett.; (United States), Vol. 56:16
- Country of Publication:
- United States
- Language:
- English
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