Journal article

The phase transitions of the random-cluster and Potts models on slabs with $q \geq 1$ are sharp

    2018
Published in:
  • Electronic Journal of Probability. - 2018, vol. 23
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
  • English
Classification
Mathematics
License
License undefined
Identifiers
Persistent URL
https://folia.unifr.ch/unifr/documents/307253
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