Percolation in strongly correlated systems: The massless Gaussian field |
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| Authors: | Jean Bricmont Joel L Lebowitz Christian Maes |
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| Institution: | (1) Department of Mathematics and Physics, Rutgers University, 08903 New Brunswick, New Jersey;(2) Present address: Physique Théorique, UCL, B-1348 Louvain-La-Neuve, Belgium;(3) Aspirant NFWO, Instituut voor Theoretische Fysika, K.U. Leuven, B-3030 Leuven, Belgium |
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| Abstract: | We derive a number of new results for correlated nearest neighbor site percolation onZ
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 – , has a nontrivial percolation behavior: sites on whichS
x
 h percolate if and only ifh
c
. with0
c
<  . This provides the first rigorous example of a percolation transition in a system with infinite susceptibility. |
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| Keywords: | Percolation weak and strong correlation symmetry breaking massless harmonic crystal |
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