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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- massless harmonic crystal
- symmetry breaking
- weak and strong correlation