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Correlation inequalities of GKS type for the Potts model

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https://www.repository.cam.ac.uk/handle/1810/254942

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Published version (706.43 KB)
 Accepted version (140.07 KB) (Embargoed until: 2100-01-01)

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Article

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Authors

Grimmett, Geoffrey  ORCID logo  https://orcid.org/0000-0001-7646-3368

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.

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Keywords

Griffiths inequality, GKS inequality, Ising model, Potts model, random-cluster model, angular spins

Journal Title

Mathematics and Mechanics of Complex Systems

Conference Name

Journal ISSN

2326-7186
2325-3444

Volume Title

4

Publisher

Mathematical Sciences Publishers

Publisher DOI

https://doi.org/10.2140/memocs.2016.4.327

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Sponsorship
Engineering and Physical Sciences Research Council (EP/I03372X/1)
This work was supported in part by the Engineering and Physical Sciences Research Council under grant EP/I03372X/1.

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Scholarly Works - Pure Mathematics and Mathematical Statistics
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