Planar Skyrmions at high and low density

TL;DR

This paper explores phase transitions of planar Skyrmions between crystalline and localized configurations, highlighting how potential choices influence the structure, with implications for understanding similar phenomena in three dimensions.

Contribution

It introduces two models of planar Skyrmions with different low-density configurations, providing insights into their phase behavior and analogies to three-dimensional Skyrmions.

Findings

Multi-Skyrmions form a ring at low density in the first model.

The second model exhibits crystal chunks as low-density configurations.

The second model closely resembles three-dimensional Skyrmion behavior.

Abstract

The O(3) Skyrme system in two space dimensions admits topological soliton solutions. This paper studies the transition between the high-density crystalline phase of such solitons and the low-density phase where there are multi-Skyrmions localized in space. The details depend crucially on the choice of the potential function. Two such choices are investigated: in the first system, multi-Skyrmions at low density form a ring; while in the second, there is an explicit crystal solution, and the preferred low-density configurations are chunks of this crystal. The second system is a particularly good analogue of three-dimensional Skyrmions.