Decay of two-point functions for $(d+ 1) $-dimensional percolation ...

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Decay of Two-Point Functions for Percolation, Ising and Potts Models. 485. The fact that these are (d + l)-dimensional models with ^-dimensional disorder.
Communications ΪΠ

Commun. Math. Phys. 135, 483-497 (1991)

Mathematical Physics

© Springer-Verlag 1991

Decay of Two-Point Functions for (d + l)-Dimensional Percolation, Ising and Potts Models with ^/-Dimensional Disorder Massimo Campanino* and Abel Klein** Department of Mathematics, University of California, Irvine, Irvine, CA 92717, USA Received February 5, 1990

Abstract. Let { J ( X ί y y } ( x > y y ^ z d and {Kx}xeZd be independent sets of nonnegative i.i.d.r.v.'s, denoting a pair of nearest neighbors in Zd; let β,y > 0. We consider the random systems: 1. A bond Bernoulli percolation model on Zd+1 with random occupation probabilities 1 — β ~ 2βJy> iϊt = s9x9y nearest neighbors 1i — eP ~2yKχ if11v x——v y,\t\ι—