Intrinsic conformal order revealed in geometrically confined long-range repulsive particles

TL;DR

This paper uncovers an intrinsic conformal order in long-range repulsive particle packings, showing how geometric confinement and topological defects influence their structure, with implications for designing novel materials.

Contribution

It introduces the concept of conformal order in long-range interacting systems and demonstrates its protection by topological defects, advancing understanding of particle packing organization.

Findings

Revealed intrinsic conformal order in particle packings

Identified the role of topological defects in protecting conformal order

Showed potential for creating novel particle arrangements using long-range forces

Abstract

Elucidating long-range interaction guided organization of matter is a fundamental question in physical systems covering multiple length scales. Here, based on the hexagonal disk model, we analyze the characteristic inhomogeneity created by long-range repulsions, and reveal the intrinsic conformal order in particle packings in mechanical equilibrium. Specifically, we highlight the delicate angle-preserved bending of the lattice to match the inhomogeneity condition. The revealed conformal order is found to be protected by the surrounding topological defects. These results advance our understanding on long-range interacting systems, and open the promising possibilities of using long-range forces to create particle packings not accessible by short-range forces, which may have practical consequences.