Percolation in strongly correlated systems: The massless Gaussian field

Jean Bricmont; Joel L. Lebowitz; Christian Maes

doi:10.1007/BF01009544

Percolation in strongly correlated systems: The massless Gaussian field

Jean Bricmont, Joel L. Lebowitz, Christian Maes

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36 Scopus citations

Abstract

We derive a number of new results for correlated nearest neighbor site percolation on Z^d. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance -Δ, has a nontrivial percolation behavior: sites on which S_x≥h percolate if and only if h<h_c. with 0</h_c < ∞. This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.

Original language	English (US)
Pages (from-to)	1249-1268
Number of pages	20
Journal	Journal of Statistical Physics
Volume	48
Issue number	5-6
DOIs	https://doi.org/10.1007/BF01009544
State	Published - Sep 1987

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Percolation
massless harmonic crystal
symmetry breaking
weak and strong correlation

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10.1007/BF01009544

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abstract = "We derive a number of new results for correlated nearest neighbor site percolation on Zd. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance -Δ, has a nontrivial percolation behavior: sites on which Sx≥h percolate if and only if hc. with 0c < ∞. This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.",

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T1 - Percolation in strongly correlated systems

T2 - The massless Gaussian field

AU - Bricmont, Jean

AU - Lebowitz, Joel L.

AU - Maes, Christian

PY - 1987/9

Y1 - 1987/9

N2 - We derive a number of new results for correlated nearest neighbor site percolation on Zd. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance -Δ, has a nontrivial percolation behavior: sites on which Sx≥h percolate if and only if hc. with 0c < ∞. This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.

AB - We derive a number of new results for correlated nearest neighbor site percolation on Zd. We show in particular that in three dimensions the strongly correlated massless harmonic crystal, i.e., the Gaussian random field with mean zero and covariance -Δ, has a nontrivial percolation behavior: sites on which Sx≥h percolate if and only if hc. with 0c < ∞. This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.

KW - Percolation

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KW - symmetry breaking

KW - weak and strong correlation

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