Absence of a Finite-Temperature Melting Transition in the Classical Two-Dimensional One-Component Plasma

TL;DR

This paper demonstrates that in a two-dimensional one-component plasma, a finite-temperature melting transition does not occur, with crystalline order only emerging as temperature approaches zero, supported by theoretical arguments and simulations.

Contribution

The study provides a theoretical argument and simulation evidence showing the absence of a finite-temperature melting transition in the 2D one-component plasma.

Findings

Crystalline order correlation length grows as √(1/T) at low temperatures

No finite-temperature melting transition exists in the system

Simulations confirm the theoretical predictions

Abstract

Vortices in thin-film superconductors are often modelled as a system of particles interacting via a repulsive logarithmic potential. Arguments are presented to show that the hypothetical (Abrikosov) crystalline state for such particles is unstable at any finite temperature against proliferation of screened disclinations. The correlation length of crystalline order is predicted to grow as $\sqrt{1/T}$ as the temperature $T$ is reduced to zero, in excellent agreement with our simulations of this two-dimensional system.