Percolation in strongly correlated systems: The massless Gaussian field

Jean Bricmont, Joel L. Lebowitz, Christian Maes

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


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 h<hc. with 0</hc < ∞. This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.

Original languageEnglish (US)
Pages (from-to)1249-1268
Number of pages20
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Sep 1987

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Percolation
  • massless harmonic crystal
  • symmetry breaking
  • weak and strong correlation

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