Ising models on the Lobachevsky plane

DOI10.1007/BF02097045zbMath0692.60088MaRDI QIDQ583748

Caroline Series, Yakov G. Sinai

Publication date: 1990

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

cocompact group acting on the hyperbolic planeIsing model on a latticemutually singular Gibbs states

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Phase transitions (general) in equilibrium statistical mechanics (82B26) Equilibrium statistical mechanics (82B99)

Related Items (12)

Explicit isoperimetric constants and phase transitions in the random-cluster model ⋮ The Ising model on diluted graphs and strong amenability ⋮ THE GEOMETRY OF FAREY STAIRCASES ⋮ Ising percolation in the hyperbolic plane ⋮ Continuity of the Ising phase transition on nonamenable groups ⋮ On a factor associated with the unordered phase of \(\lambda\)-model on a Cayley tree ⋮ Phase transitions on nonamenable graphs ⋮ A manifold of pure Gibbs states of the Ising model on the Lobachevsky plane ⋮ MULTIFRACTAL SPECTRUM AND THERMODYNAMICAL FORMALISM OF THE FAREY TREE ⋮ Phase Transitions and Minimal Hypersurfaces in Hyperbolic Space ⋮ Ising models on hyperbolic graphs ⋮ Von Neumann algebras generated by translation-invariant Gibbs states of the Ising model on a Bethe lattice

Cites Work

• The combinatorial structure of cocompact discrete hyperbolic groups
• Growth functions on Fuchsian groups and the Euler characteristic
• Bosonization, topological solitons and fractional charges in two- dimensional quantum field theory
• Markov random fields on an infinite tree
• Investigation of Gibbsian States for Three-Dimensional Lattice Systems
• Gibbs States on Countable Sets

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