A new computation of the critical point for the planar random-cluster model with $q\ge1$
| Autor: | Aran Raoufi, Vincent Tassion, Hugo Duminil-Copin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Random cluster 82B43 82B20 FOS: Physical sciences 01 natural sciences Critical point (mathematics) Critical point Combinatorics 010104 statistics & probability FOS: Mathematics Potts model 0101 mathematics Mathematical Physics Mathematics Phase transition Random-cluster model 010102 general mathematics Probability (math.PR) Mathematical Physics (math-ph) Sharp phase transition 60K35 82B26 Statistics Probability and Uncertainty Mathematics - Probability |
| Zdroj: | Ann. Inst. H. Poincaré Probab. Statist. 54, no. 1 (2018), 422-436 |
| Popis: | We present a new computation of the critical value of the random-cluster model with cluster weight $q\ge 1$ on $\mathbb{Z}^2$. This provides an alternative approach to the result of Beffara and Duminil-Copin. We believe that this approach has several advantages. First, most of the proof can easily be extended to other planar graphs with sufficient symmetries. Furthermore, it invokes RSW-type arguments which are not based on self-duality. And finally, it contains a new way of applying sharp threshold results which avoid the use of symmetric events and periodic boundary conditions. Comment: 16 pages, 3 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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