Kittel's molecular zipper model on Cayley trees

TL;DR

This paper extends Kittel's DNA zipper model to Cayley trees, analyzing Gibbs measures, phase transitions, and free energy, providing explicit critical temperatures and new boundary laws.

Contribution

It introduces a multidimensional version of Kittel's model on Cayley trees and characterizes Gibbs measures through boundary laws, revealing phase transition conditions.

Findings

Explicit critical temperature for phase transition identified.

General formula for free energy depending on boundary laws derived.

Concrete boundary laws and Gibbs measures constructed.

Abstract

Kittel's 1D model represents a natural DNA with two strands as a (molecular) zipper, which may 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 non-linear functional equation, with unknown functions (called boundary laws) defined on vertices of the Cayley tree. Each boundary law defines a Gibbs measure. We give 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 a phase transition (non-uniqueness of Gibbs measures) is obtained.