Extremality of the unique translation-invariant Gibbs measure for hard-core models on the Cayley tree of order \(k=3\)

DOI10.1134/S0040577921010062zbMath1467.82017OpenAlexW3176706025MaRDI QIDQ2036324

R. M. Khakimov, K. O. Umirzakova

Publication date: 29 June 2021

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577921010062

zbMATH Keywords

configurationCayley treeGibbs measurehard-core modelfertile graphtranslation-invariant measuremeasure extremality

Mathematics Subject Classification ID

Trees (05C05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Cites Work

• Unnamed Item
• Description of the translation-invariant splitting Gibbs measures for the Potts model on a Cayley tree
• Gibbs measures for the fertile three-state hard-core models on a Cayley tree
• Translation-invariant Gibbs measures for fertile three-state ``hard core models on a Cayley tree
• Extremality of translation-invariant phases for a three-state SOS-model on the binary tree
• A hard-core model on a Cayley tree: an example of a loss network
• Fertile HC models with three states on a Cayley tree
• Gibbs measures and phase transitions
• Random surfaces with two-sided constraints: An application of the theory of dominant ground states
• Graph homomorphisms and phase transitions
• Gibbs Measures on Cayley Trees
• Gibbs States on Countable Sets
• Fuzzy transformations and extremality of Gibbs measures for the potts model on a Cayley tree
• Fast mixing for independent sets, colorings, and other models on trees
• Additional Limit Theorems for Indecomposable Multidimensional Galton-Watson Processes
• A Three State Hard-Core Model on a Cayley Tree