Gradient Gibbs measures for the SOS model with countable values on a Cayley tree

DOI10.1214/19-EJP364zbMath1431.82014arXiv1902.04909MaRDI QIDQ2279297

Florian Henning, Christof Külske, Arnaud Le Ny, Utkir A. Rozikov

Publication date: 12 December 2019

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.04909

zbMATH Keywords

Cayley treeGibbs measureSOS modelgradient Gibbs measurestree-indexed Markov chainboundary law

Mathematics Subject Classification ID

Trees (05C05) 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) Statistical mechanics of magnetic materials (82D40)

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A HC model with countable set of spin values: Uncountable set of Gibbs measures ⋮ Convergence of deterministic growth models ⋮ Mirror symmetry of height-periodic gradient Gibbs measures of an SOS model on Cayley trees ⋮ Gibbs measures for HC-model with a cuountable set of spin values on a Cayley tree ⋮ Existence of gradient Gibbs measures on regular trees which are not translation invariant ⋮ Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees ⋮ Extremal inhomogeneous Gibbs states for SOS-models and finite-spin models on trees ⋮ Fixed points of an infinite dimensional operator related to Gibbs measures ⋮ Coexistence of localized Gibbs measures and delocalized gradient Gibbs measures on trees ⋮ Ground states for the Potts model with competing interactions and a countable set of spin values on a Cayley tree ⋮ Gradient Gibbs measures of an SOS model on Cayley trees: 4-periodic boundary laws ⋮ Invariance property on group representations of the Cayley tree and its applications ⋮ Gradient Gibbs measures for the SOS model with integer spin values on a Cayley tree

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