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

Abstract

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.

Authors:
;
Publication Date:
Research Org.:
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853
OSTI Identifier:
5920710
DOE Contract Number:
AC02-83ER13044
Resource Type:
Journal Article
Resource Relation:
Journal Name: Phys. Rev. Lett.; (United States); Journal Volume: 56:16
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; TRANSPORT THEORY; MEAN-FIELD THEORY; PROBABILITY; 657006* - Theoretical Physics- Statistical Physics & Thermodynamics- (-1987)

Citation Formats

Chayes, J.T., and Chayes, L.. Inequality for the infinite-cluster density in Bernoulli percolation. United States: N. p., 1986. Web. doi:10.1103/PhysRevLett.56.1619.
Chayes, J.T., & Chayes, L.. Inequality for the infinite-cluster density in Bernoulli percolation. United States. doi:10.1103/PhysRevLett.56.1619.
Chayes, J.T., and Chayes, L.. Mon . "Inequality for the infinite-cluster density in Bernoulli percolation". United States. doi:10.1103/PhysRevLett.56.1619.
@article{osti_5920710,
title = {Inequality for the infinite-cluster density in Bernoulli percolation},
author = {Chayes, J.T. and Chayes, L.},
abstractNote = {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.},
doi = {10.1103/PhysRevLett.56.1619},
journal = {Phys. Rev. Lett.; (United States)},
number = ,
volume = 56:16,
place = {United States},
year = {Mon Apr 21 00:00:00 EST 1986},
month = {Mon Apr 21 00:00:00 EST 1986}
}
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