Geodesic
Holliday junctions in the HC Blume--Capel model in ``one case'' on DNA
Nanosistemy: fizika, himiâ, matematika, Tome 12 (2021) no. 5, pp. 563-568.

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We consider a DNA as a configuration of HC Blume–Capel model and embed it on a path of Cayley tree. To study thermodynamic properties of the model of DNAs, we describe the corresponding translation-invariant Gibbs measures (TIGM) of the model on the Cayley tree. It is shown that, for $k\ge2$, for any temperature $T>0$ there is a unique TIGM. Using these results, we study the distributions of the Holliday junctions DNA. For very high and very low temperatures, we give stationary distributions and typical configurations of the Holliday junctions.
Keywords: DNA, Cayley tree, Blume–Capel model, Gibbs measure, Holliday junction. 
@article{NANO_2021_12_5_a2,
     author = {N. M. Khatamov},
     title = {Holliday junctions in the {HC} {Blume--Capel} model in ``one case'' on {DNA}},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {563--568},
     publisher = {mathdoc},
     volume = {12},
     number = {5},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2021_12_5_a2/}
}
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N. M. Khatamov. Holliday junctions in the HC Blume--Capel model in ``one case'' on DNA. Nanosistemy: fizika, himiâ, matematika, Tome 12 (2021) no. 5, pp. 563-568. http://geodesic.mathdoc.fr/item/NANO_2021_12_5_a2/