Gibbs measures of the Blume-Emery-Griffiths model on the Cayley tree

DOI10.1007/s11040-023-09448-7OpenAlexW4323048098MaRDI QIDQ2689839

U. U. Qayumov, Farhod Halimjonovich Haydarov, Golibjon Isroilovich Botirov

Publication date: 14 March 2023

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11040-023-09448-7

zbMATH Keywords

Cayley treeGibbs measuretranslation invariantBlume-Emery-Griffiths model

Mathematics Subject Classification ID

Trees (05C05) Phase transitions (general) in equilibrium statistical mechanics (82B26) Renormalization group methods in equilibrium statistical mechanics (82B28) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Cites Work

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• Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree
• Gibbs measures and phase transitions.
• Uniqueness of the Gibbs state of the BEG model in the disordered region of parameters
• Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree
• Ground states for the Potts model with competing interactions and a countable set of spin values on a Cayley tree
• New condition on uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree
• Potts model with competing interactions on the Cayley tree: The contour method
• Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model
• Gibbs Measures on Cayley Trees

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