Geodesic
The phase transition for the three-state SOS model with one-level competing interactions on the binary tree
Nanosistemy: fizika, himiâ, matematika, Tome 16 (2025) no. 2, pp. 134-141

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In this paper, we consider a three-state solid-on-solid (SOS) model with two competing interactions (nearest-neighbor, one-level next-nearest-neighbor) on the Cayley tree of order two. We show that at some values of the parameters the model exhibits a phase transition. We also prove that for the model under some conditions there is no two-periodic Gibbs measures.
Keywords: cayley tree, Gibbs measure, SOS model, competing interactions. 
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     author = {Obid Sh. Karshiboev and Muzaffar M. Rahmatullaev},
     title = {The phase transition for the three-state {SOS} model with one-level competing interactions on the binary tree},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {134--141},
     publisher = {mathdoc},
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     number = {2},
     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2025_16_2_a1/}
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Obid Sh. Karshiboev; Muzaffar M. Rahmatullaev. The phase transition for the three-state SOS model with one-level competing interactions on the binary tree. Nanosistemy: fizika, himiâ, matematika, Tome 16 (2025) no. 2, pp. 134-141. http://geodesic.mathdoc.fr/item/NANO_2025_16_2_a1/