Geodesic
Translation-invariant Gibbs measures for the mixed spin-$1/2$ and spin-$1$ Ising model with an external field on a Cayley tree
Nanosistemy: fizika, himiâ, matematika, Tome 15 (2024) no. 5, pp. 576-585.

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Phase transitions of the mixed spin-$1/2$ and spin-$1$ Ising model under the presence of an external field on the general order Cayley tree are investigated within the framework of the tree-indexed Markov chains. We find the conditions that ensure the existence of at least three translation-invariant Gibbs measures for the model on the Cayley tree of order $k$. We are able to solve the model exactly on the binary tree $(k=2)$ under the specific external field. The main attention is paid to the systematic study of the structure of the set of the Gibbs measures. We find the extremality and non-extremality regions of the disordered phase of the model on the binary tree.
Keywords: mixed-spin Ising model; external field; Cayley tree; Gibbs measures. 
@article{NANO_2024_15_5_a1,
     author = {Muzaffar M. Rahmatullaev and Dilshod O. Egamov},
     title = {Translation-invariant {Gibbs} measures for the mixed spin-$1/2$ and spin-$1$ {Ising} model with an external field on a {Cayley} tree},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {576--585},
     publisher = {mathdoc},
     volume = {15},
     number = {5},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2024_15_5_a1/}
}
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Muzaffar M. Rahmatullaev; Dilshod O. Egamov. Translation-invariant Gibbs measures for the mixed spin-$1/2$ and spin-$1$ Ising model with an external field on a Cayley tree. Nanosistemy: fizika, himiâ, matematika, Tome 15 (2024) no. 5, pp. 576-585. http://geodesic.mathdoc.fr/item/NANO_2024_15_5_a1/