Modeling Clusters of Repulsive Particles

The subject of the study is a classical two-dimensional system of particles repelling as quadrupoles v(r) = D ^2 / r^5, also as Rydberg atoms repelling according to the law C^6 / r^6, and confined by a quadratic potential. Appropriate melting characteristics and potential barrier values as well as ground state configurations are found for clusters of N ≤ 40 particles. The melting of clusters is studied using molecular dynamic methods. Is that found that in mesoscopic clusters with N < 37 a hierarchy of phase transitions occurs: at lower temperatures, orientational melting between shells can be observed, while at higher temperatures particle exchange between shells begins and the shell structure of the cluster disappears. For «magic» and macroscopic clusters with N> 37, orientational melting takes place only for the outer shell.