Kittel’s molecular zipper model on Cayley trees-Reference-Cited by-同舟云学术

Kittel’s molecular zipper model on Cayley trees

Published:2023-10-21 Issue:01 Volume:36 Page:
ISSN:0129-055X
Container-title:Reviews in Mathematical Physics
language:en
Short-container-title:Rev. Math. Phys.

Author:

Rozikov U. A.¹²³^ORCID

Affiliation:

1. Scientific Laboratory of Algebra and its Applications, V. I. Romanovskiy Institute of Mathematics, 9, Universitet Str., 100174, Tashkent, Uzbekistan

2. Central Asian University, 264, Milliy Bog St, 111221, Tashkent, Uzbekistan

3. National University of Uzbekistan, 4, Universitet Str., 100174, Tashkent, Uzbekistan

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.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129055X23500344

Reference12 articles.

1. On the uniqueness of Gibbs measure in the Potts model on a Cayley tree with external field

2. General Non-Existence Theorem for Phase Transitions in One-Dimensional Systems with Short Range Interactions, and Physical Examples of Such Transitions

3. Gibbs Measures and Phase Transitions

4. Phase Transition of a Molecular Zipper