The polarization problem for the honeycomb structure

2025/09/29 by Faulhuber, Markus
#52C15 #74G65 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2509.24687

Abstract

We study the polarization problem in dimension 2 for the honeycomb structure and compare it to the maximal polarization lattice, the hexagonal lattice. As expected, the hexagonal lattice has higher polarization than the honeycomb at all densities.

Citations

• Polarization of lattices: Stable cold spots and spherical designs
• On polarization of spherical codes and designs
• A variational principle for Gaussian lattice sums
• On the optimality of the rock-salt structure among lattices with charge distributions
• Polarization problem on a higher-dimensional sphere for a simplex
• Unconstrained polarization (Chebyshev) problems: basic properties and Riesz kernel asymptotics
• Universal optimality of the E₈ and Leech lattices and interpolation formulas
• Optimal discrete measures for Riesz potentials
• Sur les fonctions absolument monotones

Related

• The Hexagonal Tiling Honeycomb
• The Polarized Structure Function g₂: A Lattice Study Revisited
• Polarization of lattices: Stable cold spots and spherical designs
• Macroscopic Polarization from Electronic Wavefunctions
• Revisiting the theory of crystal polarization: The downside of employing the periodic boundary conditions