ISSN:
1572-9613
Keywords:
Random-cluster model
;
Ising model
;
Potts model
;
comparison inequality
;
BK inequality
;
FKG inequality
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract A principal technique for studying percolation, (ferromagnetic) Ising, Potts, and random-cluster models is the FKG inequality, which implies certain stochastic comparison inequalities for the associated probability measures. The first result of this paper is a new comparison inequality, proved using an argument developed elsewhere in order to obtain strict inequalities for critical values. As an application of this inequality, we prove that the critical pointp c (q) of the random-cluster model with cluster-weighting factorq (≥1) is strictly monotone inq. Our second result is a “BK inequality” for the disjoint occurrence of increasing events, in a weaker form than that available in percolation theory.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02180133
Permalink
