Geometric critical exponent inequalities for general random cluster models

1987 ◽  
Vol 49 (3-4) ◽  
pp. 841-847 ◽  
Author(s):  
Hal Tasaki
Keyword(s):  
Critical Exponent ◽  
Cluster Models ◽  
Random Cluster ◽  
Critical Exponent Inequalities ◽  
Random Cluster Models

UPPER BOUND ON THE TRUNCATED CONNECTIVITY IN ONE-DIMENSIONAL β/|x–y|2 PERCOLATION MODELS AT β>1

1995 ◽  
Vol 07 (05) ◽  
pp. 723-742 ◽  
Author(s):  
DOMINGOS H.U. MARCHETTI
Keyword(s):  
Upper Bound ◽  
Weighting Factor ◽  
Cluster Models ◽  
One Dimensional ◽  
Random Cluster ◽  
Random Cluster Models

We consider one-dimensional Fortuin-Kasteleyn percolation models generated by the bond occupation probabilities [Formula: see text] and weighting factor κ. For any β>1 and κ≥1 the percolation density M is known to be strictly positive provided p is sufficiently close to 1. We prove that, under these assumptions, the following upper bound for the truncated connectivity [Formula: see text] holds with [Formula: see text] where [Formula: see text] as [Formula: see text]. This result extends Imbrie-Newman’s upper bound to independent percolation models (κ=1) and random-cluster models with non-integer values of κ.

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