The phase transitions of the random-cluster and Potts models on slabs with $q \geq 1$ are sharp
- Manolescu, Ioan Université de Fribourg, Switzerland
- Raoufiï, Aran Institut des Hautes Études Scientifiques, France
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2018
Published in:
- Electronic Journal of Probability. - 2018, vol. 23, p. 1-25
English
We prove sharpness of the phase transition for the random-cluster model with q≥1 on graphs of the form S:=G×S, where G is a planar lattice with mild symmetry assumptions, and S a finite graph. That is, for any such graph and any q≥1, there exists some parameter pc=pc(S,q), below which the model exhibits exponential decay and above which there exists a.s. an infinite cluster. The result is also valid for the random-cluster model on planar graphs with long range, compactly supported interaction. It extends to the Potts model via the Edwards-Sokal coupling.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 323412
- DOI 10.1214/17-EJP86
- Persistent URL
- https://folia.unifr.ch/unifr/documents/307253
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