BKT in Phyllotaxis
Abstract
We discuss a two-parameter renormalization group (RG) consideration of a phyllotaxis model in the framework of the ``energetic approach'' proposed by L. Levitov in 1991. Following L. Levitov, we consider an equilibrium distribution of strongly repulsive particles on the surface of a finite cylinder and study the redistribution of these particles when the cylinder is squeezed along its axis. We construct explicitly the -function of a given system in terms of the modular Dedekind -function. On basis of this -function we derive the equations describing the RG flow in the vicinity of the bifurcation points between different lattices. Analyzing the structure of RG equations, we claim emergence of Berezinskii-Kosterlitz-Thouless (BKT) transitions at strong compression of the cylinder.
Keywords
Cite
@article{arxiv.2310.05580,
title = {BKT in Phyllotaxis},
author = {Ana Flack and Sergei Nechaev},
journal= {arXiv preprint arXiv:2310.05580},
year = {2023}
}
Comments
13 pages, 5 figures; On the basis of the talk delivered by one of authors (S.N.) at the workshop "Statistical mechanics and its applications'', Dilijan, Armenia (October 2022). arXiv admin note: substantial text overlap with arXiv:2304.07640