Inequality for the infinite-cluster density in Bernoulli percolation

Journal Article · Mon Apr 21 04:00:00 EST 1986 · Phys. Rev. Lett.; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.56.1619· OSTI ID:5920710

Chayes, J T; Chayes, L

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), Journal Name: Phys. Rev. Lett.; (United States) Vol. 56:16; ISSN PRLTA
• Country of Publication: United States
• Language: English

Related Subjects

657006* -- Theoretical Physics-- Statistical Physics &amp; Thermodynamics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MEAN-FIELD THEORY
PROBABILITY
TRANSPORT THEORY