Dimensional phase transitions in small Yukawa clusters

TL;DR

This study explores how small Yukawa clusters transition from one-dimensional to two-dimensional zigzag configurations, highlighting the influence of Debye shielding and well anisotropy, with experimental and theoretical agreement.

Contribution

It provides the first detailed experimental and theoretical analysis of the zigzag transition in small Yukawa clusters, emphasizing the role of Debye shielding.

Findings

Debye shielding significantly affects the transition point.

The critical number of particles for transition is lower with shielding.

A universal critical exponent for the transition is identified.

Abstract

We investigate the one- to two-dimensional zigzag transition in clusters consisting of a small number of particles interacting through a Yukawa (Debye) potential and confined in a two-dimensional biharmonic potential well. Dusty (complex) plasma clusters with $n \le 19$ monodisperse particles are characterized experimentally for two different confining wells. The well anisotropy is accurately measured, and the Debye shielding parameter is determined from the longitudinal breathing frequency. Debye shielding is shown to be important. A model for this system is used to predict equilibrium particle configurations. The experiment and model exhibit excellent agreement. The critical value of $n$ for the zigzag transition is found to be less than that predicted for an unshielded Coulomb interaction. The zigzag transition is shown to behave as a continuous phase transition from a one-dimensional to a two-dimensional state, where the state variables are the number of particles, the well anisotropy and the Debye shielding parameter. A universal critical exponent for the zigzag transition is identified for transitions caused by varying the Debye shielding parameter.