Geodesic
Holliday junctions in the~Blume--Capel model of DNA
Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 3, pp. 439-447

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We regard a DNA molecule as a configuration of the Blume–Capel model on paths in a Cayley tree. We study translation-invariant Gibbs measures (TIGMs) of the model on the Cayley tree of order two and show that there is a critical temperature $T_\mathrm{c}$ such that there exists a unique TIGM if the temperature $T>T_\mathrm{c}$, there are two TIGMs if $T=T_\mathrm{c}$, and there are three TIGMs if $T$. Each such measure describes a phase of the set of DNA molecules. We use these measures to study probability distributions of Holliday junctions in DNA molecules.
Keywords: Cayley tree, Blume–Capel model, Gibbs measure, Holliday junction. 
@article{TMF_2021_206_3_a8,
     author = {N. M. Khatamov},
     title = {Holliday junctions in {the~Blume--Capel} model of {DNA}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {439--447},
     publisher = {mathdoc},
     volume = {206},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_206_3_a8/}
}
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N. M. Khatamov. Holliday junctions in the~Blume--Capel model of DNA. Teoretičeskaâ i matematičeskaâ fizika, Tome 206 (2021) no. 3, pp. 439-447. http://geodesic.mathdoc.fr/item/TMF_2021_206_3_a8/