Sharp phase transition for the random-cluster and Potts models via decision trees
| Autor: | Aran Raoufi, Vincent Tassion, Hugo Duminil-Copin |
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| Rok vydání: | 2019 |
| Předmět: |
Probability (math.PR)
010102 general mathematics FOS: Physical sciences Monotonic function Mathematical Physics (math-ph) 01 natural sciences Upper and lower bounds Square (algebra) Combinatorics Mathematics (miscellaneous) Critical point (set theory) Product (mathematics) 0103 physical sciences Gaussian free field FOS: Mathematics 010307 mathematical physics Continuum (set theory) 0101 mathematics Statistics Probability and Uncertainty Mathematics - Probability Mathematical Physics Potts model Mathematics |
| Zdroj: | Annals of Mathematics. 189 |
| ISSN: | 0003-486X |
| DOI: | 10.4007/annals.2019.189.1.2 |
| Popis: | We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their random-cluster representations. More precisely, we prove that 1. For the Potts model on transitive graphs, correlations decay exponentially fast for $\beta Comment: 16 pages, 3 figures |
| Databáze: | OpenAIRE |
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