Generalized Flory Theory for Rotational Symmetry Breaking of Complex Macromolecules

TL;DR

This paper introduces a generalized Flory theory to analyze how complex macromolecules with branches and cycles undergo spontaneous rotational symmetry breaking as self-repulsion increases, linking topological structure to density distribution.

Contribution

The paper develops a variational mean-field approach combining Flory theory and Laplacian matrix analysis to describe symmetry breaking in complex macromolecules.

Findings

Transition from isotropic to anisotropic density distribution at a critical self-repulsion strength.

Density distribution determined by Laplacian matrix eigenvalues and eigenvectors.

Free energy landscape exhibits multiple minima indicating complex structural behavior.

Abstract

We report on spontaneous rotational symmetry breaking in a minimal model of complex macromolecules with branches and cycles. The transition takes place as the strength of the self-repulsion is increased. At the transition point, the density distribution transforms from isotropic to anisotropic. We analyze this transition using a variational mean-field theory that combines the Gibbs-Bogolyubov-Feynman inequality with the concept of the Laplacian matrix. The density distribution of the broken symmetry state is shown to be determined by the eigenvalues and eigenvectors of this Laplacian matrix. Physically, this reflects the increasing role of the underlying topological structure in determining the density of the macromolecule when repulsive interactions generate internal tension Eventually, the variational free energy landscape develops a complex structure with multiple competing minima.