Geodesic
Translation-invariant Gibbs measures for fertile three-state ``hard core'' models on a~Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 3, pp. 441-449

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We consider fertile three-state "hard core" models with the activity parameter $\lambda>0$ on an order-three Cayley tree. It is known that there exist four types of such models: in two of them, the translation-invariant Gibbs measure is unique for $\lambda>0$, and in the other two, a value $\lambda_\mathrm{cr}$ is found such that there exist only three translation-invariant Gibbs measures for $\lambda>\lambda_\mathrm{cr}$ and a single translation-invariant Gibbs measure for $\lambda\le\lambda_\mathrm{cr}$.
Keywords: Cayley tree, hard core model, Gibbs measure, translation-invariant measure.
Mots-clés : configuration 
@article{TMF_2015_183_3_a6,
     author = {R. M. Khakimov},
     title = {Translation-invariant {Gibbs} measures for fertile three-state ``hard core'' models on {a~Cayley} tree},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {441--449},
     publisher = {mathdoc},
     volume = {183},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_183_3_a6/}
}
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R. M. Khakimov. Translation-invariant Gibbs measures for fertile three-state ``hard core'' models on a~Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 183 (2015) no. 3, pp. 441-449. http://geodesic.mathdoc.fr/item/TMF_2015_183_3_a6/