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We consider two models of interacting DNA molecules: First is (four parametric) bubble coalescence model in interacting DNAs (shortly: BCI-DNA). Second is (three parametric) bubble coalescence model in a condensed DNA molecules (shortly BCC-DNA). To study bubble coalescence thermodynamics of BCI-DNA and BCC-DNA models we use methods of statistical physics. Namely, we define Hamiltonian of each model and give their translation-invariant Gibbs measures (TIGMs). For the first model, we find parameters such that corresponding Hamiltonian has up to three TIGMs (three phases of system) biologically meaning existence of three states: "No bubble coalescence", "Dominated soft zone", "Bubble coalescence". For the second model, we show that for any (admissible) parameters, this model has unique TIGM. This is a state where "No bubble coalescence" phase dominates. [ABSTRACT FROM AUTHOR]

In this paper, we give a systematic review of the theory of Gibbs measures of Potts model on Cayley trees (developed since 2013) and discuss many applications of the Potts model to real world situations: mainly biology, physics, and some examples of alloy behavior, cell sorting, financial engineering, flocking birds, flowing foams, image segmentation, medicine, sociology, etc. [ABSTRACT FROM AUTHOR]

In the Letter we investigate aq-component models on a Cayley tree. The main goal of the Letter is to develop a ‘‘contour’’ argument on Cayley tree. We define contours and study some properties of these contours. Using a contour argument we show existence ofqdifferent Gibbs measures for severalq-component models. [ABSTRACT FROM AUTHOR]