Holliday junctions in the set of DNA molecules for new translation-invariant Gibbs measures of the Potts model

N. M. Khatamov^a, N. N. Malikov<sup>b

a</sup> Romanovskiy Institute of Mathematcs, Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan
^b Namangan State University, Namangan, Uzbekistan

Abstract: We consider a DNA molecule as a configuration of the Potts model on paths of the Cayley tree. For this model, we study new translation-invariant Gibbs measures. We find exact values of the parameter establishing the uniqueness of translation-invariant Gibbs measures. Each such measure describes the state (phase) of a set of DNA molecules. These Gibbs measures are used to study probability distributions of the Holliday junctions in the DNA molecules.

Keywords: Cayley tree, Potts model, Gibbs measure, Holliday junction.

Received: 07.04.2023
Revised: 02.05.2023

DOI: 10.4213/tmf10515

 English version: Theoretical and Mathematical Physics, 2024, 218:2, 346–356

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