1. Kittel's molecular zipper model on Cayley trees.
- Author
-
Rozikov, U. A.
- Subjects
- *
PHASE transitions , *CRITICAL temperature , *FUNCTIONAL equations , *NONLINEAR equations , *TREES - Abstract
Kittel's 1D model represents a natural DNA with two strands as a (molecular) zipper, which may be separated as the temperature is varied. We define multidimensional version of this model on a Cayley tree and study the set of Gibbs measures. We reduce description of Gibbs measures to solving of a nonlinear functional equation, with unknown functions (called boundary laws) defined on vertices of the Cayley tree. Each boundary law defines a Gibbs measure. We give a general formula of free energy depending on the boundary law. Moreover, we find some concrete boundary laws and corresponding Gibbs measures. Explicit critical temperature for occurrence of a phase transition (non-uniqueness of Gibbs measures) is obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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