BKT in Phyllotaxis

Ana Flack; Sergei Nechaev

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arXiv · 2310.05580

BKT in Phyllotaxis

Ana Flack·Sergei Nechaev

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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 $\beta$-function of a given system in terms of the modular Dedekind $\eta$-function. On basis of this $\beta$-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.

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Ana Flack, Sergei Nechaev. 2023-10-09. BKT in Phyllotaxis. https://arxiv.org/abs/2310.05580

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