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

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

Griffiths inequality, GKS inequality, Ising model, Potts model, random-cluster model, angular spins
Mathematical Subject Classification 2010
Primary: 82B20, 60K35
Received: 3 December 2015
Accepted: 28 March 2016
Published: 17 December 2016

Communicated by Raffaele Esposito
Geoffrey R. Grimmett
Statistical Laboratory
Centre for Mathematical Sciences
University of Cambridge
United Kingdom