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 −Δ, has a nontrivial percolation behavior: sites on whichS x ⩾h percolate if and only ifh<h c . with0</h c < ∞. This provides the first rigorous example of a percolation transition in a system with infinite susceptibility.
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Bricmont, J., Lebowitz, J.L. & Maes, C. Percolation in strongly correlated systems: The massless Gaussian field. J Stat Phys 48, 1249–1268 (1987). https://doi.org/10.1007/BF01009544
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DOI: https://doi.org/10.1007/BF01009544