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Title: Inequality for the infinite-cluster density in Bernoulli percolation

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.
Publication Date:
OSTI Identifier:
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Phys. Rev. Lett.; (United States); Journal Volume: 56:16
Research Org:
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853
Country of Publication:
United States
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; TRANSPORT THEORY; MEAN-FIELD THEORY; PROBABILITY 657006* -- Theoretical Physics-- Statistical Physics & Thermodynamics-- (-1987)