The density profile of a Coulomb plasma on a cylinder: boundary oscillations

TL;DR

This paper uses Monte Carlo simulations to study boundary density oscillations and defect suppression in a 2D Coulomb plasma on a cylinder, revealing insights into phase transitions and boundary-bulk correlations.

Contribution

It introduces a detailed analysis of boundary effects and defect behavior in a 2D Coulomb plasma confined to a cylindrical geometry, with new correlation functions linking boundary and bulk properties.

Findings

Boundary density oscillations depend on boundary conditions.

Topological defects are exponentially suppressed in the crystalline phase.

An oriented correlation function links boundary profiles with bulk correlations.

Abstract

We present Monte Carlo simulations of the two-dimensional one-component plasma (2D OCP) confined to a cylindrical geometry, focusing on density profiles, fluctuations, and their connection to bulk correlation functions. The cylindrical geometry eliminates geometric frustration, allowing for a precise study of boundary density oscillations, the dependence on boundary conditions, and their relationship to the melting transition and triangular lattice structure. By triangulating particle configurations, we quantify the exponential suppression of topological defects in the crystalline phase. Furthermore, we propose an oriented correlation function that better links boundary density profiles with bulk correlation functions, motivating anisotropic generalizations of the phase-field crystal (PFC) model. These results provide new insights into the interplay between boundary effects, bulk correlations, and phase transitions in the 2D OCP.