Energy and symmetry of ordered 2D clusters in a parabolic confinement

Abstract

We report an experimental study of 2D dipole clusters formed by small magnetic particles floating at the air-water interface. The particles form hexagonally ordered clusters due to interplay between dipole-dipole repulsion and confining external forces. Optical images of the clusters allow determination of area S, total energy E, and the chemical potential for different particle numbers N<130. Asymptotic expressions for E(N), S(N) account fairly well for the smooth part of our experimental results. However, on top of the smooth dependences we observe quasiperiodic fluctuations with dips at ``magic&#39;&#39; numbers corresponding to particularly symmetric cluster configurations. The magnitude and occurrence of these fluctuations are related to the symmetry of the cluster and to the center of mass position. This is in full agreement with the recent prediction of Koulakov and Shklovskii for Wigner crystal island.