Melting Transition of Vortex Lattice in Point Vortex Systems

TL;DR

This paper investigates the melting transition of vortex lattices in point vortex systems through numerical simulations, revealing a progression from ordered lattice to layered and then liquidlike states as energy increases.

Contribution

It introduces a mean-field approximation to interpret the melting transition in layered vortex lattice structures based on simulation results.

Findings

Vortex lattice becomes irregular with increased energy.

Layered structures emerge at intermediate energies.

Liquidlike states form at high energy levels.

Abstract

Point vortices take a triangular lattice structure in a rotating system as a minimum energy state. We perform a numerical simulation of point vortex systems using initial conditions indicating that the triangular lattice is randomly perturbed. The total energy increases with the magnitude of the perturbation. When the energy is increased, the vortex lattice becomes irregular and a layered structure appears. When the energy is further increased, the layered structure disappears and a liquidlike state appears. We interpret the melting transition with a mean-field approximation for layered structures.