The boundary density profile of a Coulomb droplet. Freezing at the edge

We revisit the problem of computing the boundary density profile of a droplet of two-dimensional one-component plasma (2D OCP) with logarithmic interaction between particles in a confining harmonic potential. At a sufficiently low temperature, but still in the liquid phase, the density exhibits oscillations as a function of the distance to the boundary of the droplet. We obtain the density profile numerically using Monte-Carlo simulations of the 2D OCP. We argue that the decay and period of those oscillations can be explained within a picture of the Wigner crystallization near the boundary, where the crystal is gradually melted with the increasing distance to the boundary.

Automated summary

In the study of two-dimensional one-component plasma, we found through numerical simulations that at sufficiently low temperatures, but still in the liquid phase, the density in the droplet exhibits oscillations near the boundary. These oscillations decay and have a certain period, which can be explained by the Wigner crystallization near the boundary, where the crystal gradually melts with increasing distance to the boundary.