  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.
