Correlation inequalities for the Potts model
Geoffrey R. Grimmett
TL;DR
This paper establishes correlation inequalities for ferromagnetic Potts models with external fields, utilizing the random-cluster representation and FKG inequality, extending previous results and including GKS-type inequalities for specific spin spaces.
Contribution
It introduces new correlation inequalities for the Potts model that generalize and simplify earlier results, incorporating the random-cluster framework and GKS inequalities.
Findings
Extended correlation inequalities for the Potts model.
Simplified proofs of existing inequalities.
Inclusion of GKS-type inequalities for specific spin spaces.
Abstract
Correlation inequalities are presented for ferromagnetic Potts models with external field, using the random-cluster representation of Fortuin and Kasteleyn, together with the FKG inequality. These results extend and simplify earlier inequalities of Ganikhodjaev and Razak, and also of Schonmann, and include GKS-type inequalities when the spin-space is taken as the set of th roots of unity.
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