Holliday junctions in the Blume–Capel model of DNA

Abstract

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 $$T<T_{ \mathrm{c} }$$ . 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.

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DOI

10.1134/s0040577921030090

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