#### Vol. 4, No. 3-4, 2016

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Correlation inequalities for the Potts model

### Geoffrey R. Grimmett

Vol. 4 (2016), No. 3-4, 327–334
##### 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 $q$-th roots of unity.

 Dedicated in friendship to Lucio Russo
##### Keywords
Griffiths inequality, GKS inequality, Ising model, Potts model, random-cluster model, angular spins
##### Mathematical Subject Classification 2010
Primary: 82B20, 60K35