Effects of three-body interactions on structural phases of classical twodimensional cluster

Abstract

When a physical system has many interacting constituents, many-body terms will arise in the Hamiltonian, besides the usual two-body interactions. These terms are often ignored in numerical studies due to their high computational cost. However, many-body terms are responsible for important corrections in charged colloidal systems and promote structural changes in clusters of Abrikosov vortices in superconductors. The main goal of this work is to determine the effect the addition of a three-body term has on the properties of two-dimensional clusters of classical interacting particles. In order to understand such effect, we carried out semi-analytical calculations and numerical minimization of the system free energy, using a simulated annealing scheme based on the Langevin dynamics. We considered 𝑁 particles (3 ≤ 𝑁 ≤ 50) confined in a parabolic potential and interacting via a pair potential. We considered three of the most studied pair potentials: logarithmic, Coulomb and Yukawa. The novelty in our study consisted in the addition of a short-ranged Gaussian three-body interaction potential with tunable amplitude. The obtained configurations were compared with the typical case in which the particles interact only via a pair potential. In this last situation, we recover the typical concentric rings of particles, widely found in the literature. With the addition of the three-body interaction, our findings include changes in the ring occupation numbers and the emergence of a first-order like transition associated with the bistability phenomenon due to the competition between the two- and three-body potentials. This transition is accompanied by a sudden cluster compaction, especially in the 𝑁 > 20 range, for all two-body potentials, and a phase separation effect starting around 𝑁 = 40, in which the initial single cluster was divided into smaller ones. These results indicate that the three-body term in the interaction potential of many confined particles can induce dramatic changes in the equilibrium configurations and, therefore, should not be ignored in those particle systems.