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We define a DNA as a sequence of $1, 2$'s and embed it on a path of Cayleytree in such a way that each vertex of the Cayley tree belongs only to one ofDNA and each DNA has its own countably many set of neighboring DNAs. TheHamiltonian of this set of DNAs is a model with two spin values considered asDNA base pairs. We describe translation invariant Gibbs measures (TIGM) of themodel on the Cayley tree of order two and use them to study thermodynamicproperties of the model of DNAs. We show that there is a critical temperature$T_{\rm c}$ such that (i) if temperature $T\geq T_{\rm c}$ then there existsunique TIGM; (ii) if $T<T_{\rm c}$ then there are three TIGMs. Each TIGM givesa phase of the set of DNAs. In case of very high and very low temperatures wegive stationary distributions and typical configurations of the model.

Thermodynamics of interacting system of DNAs