Sharp phase transition for the random-cluster and Potts models via decision trees

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...

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Bibliographic Details
Published in:arXiv.org 2018-12
Main Authors: Duminil-Copin, Hugo, Raoufi, Aran, Tassion, Vincent
Format: Article
Language:English
Subjects:
Beta decay
Boolean algebra
Clusters
Critical point
Decay rate
Decision trees
Graphs
Inequality
Lattices
Lower bounds
Percolation
Phase transitions
Probability theory
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Summary: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
ISSN:2331-8422