Abstract
We develop a new analysis of the order-disorder transition in ferromagnetic Potts models for large numberq 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 ofq) 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.
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Communicated by Ya. G. Sinaï
Laboratoire Propre du CNRS: LP 7061
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Laanait, L., Messager, A., Miracle-Sole, S. et al. Interfaces in the Potts model I: Pirogov-Sinai theory of the Fortuin-Kasteleyn representation. Commun.Math. Phys. 140, 81–91 (1991). https://doi.org/10.1007/BF02099291
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DOI: https://doi.org/10.1007/BF02099291