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

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.