论文标题
DNA相互作用系统的热力学
Thermodynamics of interacting system of DNAs
论文作者
论文摘要
我们将DNA定义为$ 1，2 $的序列，并将其嵌入到Cayley树的路径上，以使Cayley树的每个顶点仅属于DNA之一，并且每个DNA都有其自身的许多相邻DNA集合。这组DNA的哈密顿量是一个模型，其两个自旋值被视为DNA碱基对。我们描述了第二阶cayley树上模型的翻译吉布斯度量（TIGM），并使用它们来研究DNA模型的热力学特性。我们表明存在关键温度$ t _ {\ rm c} $，因此（i）如果温度$ t \ geq t _ {\ rm c} $，则存在唯一的提格。 （ii）如果$ t <t _ {\ rm c} $，则有三个tigms。每个TIGM给出了一组DNA的阶段。如果温度很高和非常低的温度，我们提供固定分布和模型的典型配置。
We define a DNA as a sequence of $1, 2$'s and embed it on a path of Cayley tree in such a way that each vertex of the Cayley tree belongs only to one of DNA and each DNA has its own countably many set of neighboring DNAs. The Hamiltonian of this set of DNAs is a model with two spin values considered as DNA base pairs. We describe translation invariant Gibbs measures (TIGM) of the model on the Cayley tree of order two and use them to study thermodynamic properties 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 exists unique TIGM; (ii) if $T<T_{\rm c}$ then there are three TIGMs. Each TIGM gives a phase of the set of DNAs. In case of very high and very low temperatures we give stationary distributions and typical configurations of the model.
