Almost sure quasilocality fails for the random-cluster model on a tree.

DOI10.1007/BF02174134zbMath1081.82520OpenAlexW1991617554MaRDI QIDQ1593468

Olle Häggström

Publication date: 16 January 2001

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02174134

zbMATH Keywords

treeIsing modelGibbs measurerandom-cluster modelquasilocalityalmost sure quasilocality

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Phase transitions (general) in equilibrium statistical mechanics (82B26) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (5)

Graphical representations for Ising and Potts models in general external fields ⋮ Gibbs-non-Gibbs properties for evolving Ising models on trees ⋮ Coloring percolation clusters at random. ⋮ Weakly Gibbsian measures for lattice spin systems ⋮ Entropy for translation-invariant random-cluster measures

Cites Work

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• The contact process on trees
• Markov random fields on an infinite tree
• Almost sure quasilocality in the random cluster model.
• Pathological behavior of renormalization-group maps at high fields and above the transition temperature.
• Projections of Gibbs measures may be non-Gibbsian
• A note on the projection of Gibbs measures
• The random-cluster model on a homogeneous tree
• The stochastic random-cluster process and the uniqueness of random-cluster measures
• Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.
• Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory
• The fuzzy Potts model

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