Interfaces in the Potts model I: Pirogov-Sinai theory of the Fortuin-Kasteleyn representation

Lahoussine Laanait, Alain Messager, Salvador Miracle-Sole, Jean Ruiz, Senya Shlosman

Research output: Contribution to journalArticlepeer-review

73 Citations (Scopus)

Abstract

We develop a new analysis of the order-disorder transition in ferromagnetic Potts models for large number q of spin states. We use the Pirogov-Sinaï theory which we adapt to the Fortuin-Kasteleyn representation of the models. This theory applies in a rather direct way in our approach and leads to a system of non-interacting contours with small activities. As a consequence, simpler and more natural techniques are found, allowing us to recover previous results on the bulk properties of the model (which then extend to non-integer values of q) and to deal with non-translation invariant boundary conditions. This will be applied in a second part of this work to study the behaviour of the interfaces at the transition point.

Original languageEnglish
Pages (from-to)81-91
Number of pages11
JournalCommunications in Mathematical Physics
Volume140
Issue number1
DOIs
Publication statusPublished - Aug 1991
Externally publishedYes

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