Ising models on hyperbolic graphs

DOI10.1007/BF02175564zbMath0926.60079OpenAlexW1969566182MaRDI QIDQ1285260

C. Chris Wu

Publication date: 18 November 1999

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

Full work available at URL: https://doi.org/10.1007/bf02175564

zbMATH Keywords

hyperbolic graphIsing modelmultiple phase transitions

Mathematics Subject Classification ID

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

Related Items

The Ising model on diluted graphs and strong amenability ⋮ Ising percolation in the hyperbolic plane ⋮ Continuity of the Ising phase transition on nonamenable groups ⋮ Ising-like models on Euclidean black holes ⋮ Thermodynamics and structure of simple liquids in the hyperbolic plane ⋮ Critical behavior in spherical and hyperbolic spaces ⋮ Phase transitions on nonamenable graphs ⋮ Continuity of percolation probability on hyperbolic graphs ⋮ Comment on: Ising models on hyperbolic graphs ⋮ The random cluster model on a general graph and a phase transition characterization of nonamenability

Cites Work

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• Ising models on the Lobachevsky plane
• Markov fields on branching planes
• The stochastic random-cluster process and the uniqueness of random-cluster measures
• Diffusions and random shadows in negatively curved manifolds
• Discontinuity of the magnetization in one-dimensional \(1/| x-y| ^ 2\) Ising and Potts models.
• Existence of a Phase Transition in Two-Dimensional and Three-Dimensional Ising Models
• On Ising's model of ferromagnetism

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