Year: 2024
Type: article
Abstract: We explore a two-parameter renormalization group (RG) within the framework of the «energetic approach» introduced by L. Levitov, for the phyllotaxis model. Our focus lies on an equilibrium distribution of strongly repulsive particles situated on the surface of a finite cylinder. We investigate how these particles redistribute as the cylinder undergoes compression along its axis. Specifically, we construct the modular-invariant β-function for the system, which is explicitly expressed in terms of the Dedekind η-function. Utilizing this β-function, we derive equations that describe the RG flow near the bifurcation points, which mark the boundaries between different lattice configurations. By analyzing the structure of these RG equations, we assert the emergence of Berezinskii – Kosterlitz – Thouless transitions under significant cylinder compression.
Author: S. K. Nechaev
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4401530209