Potts Model with Invisible Colors: Random-Cluster Representation and Pirogov–Sinai Analysis

Aernout C.D. van Enter, Giulio Iacobelli, Siamak Taati

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We study a recently introduced variant of the ferromagnetic Potts model consisting of a ferromagnetic interaction among q “visible” colors along with the presence of r non-interacting “invisible” colors. We introduce a random-cluster representation for the model, for which we prove the existence of a first-order transition for any q > 0, as long as r is large enough. When q > 1, the low-temperature regime displays a q-fold symmetry breaking. The proof involves a Pirogov–Sinai analysis applied to this random-cluster representation of the model.
Original languageEnglish
Article number1250004
Number of pages42
JournalReviews in Mathematical Physics
Issue number2
Publication statusPublished - Mar-2012


  • Potts model with invisible colors
  • biased random-cluster model
  • phase transition
  • symmetry breaking

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