Skyrmions on the Two-Sphere

TL;DR

This paper investigates static Skyrmion solutions on a two-sphere, analyzing phase transitions between high-density and low-density states as the sphere's radius varies, with implications for understanding Skyrmion behavior in curved spaces.

Contribution

It provides a detailed analysis of phase transitions of Skyrmions on a curved surface, highlighting the effects of sphere size and potential choices on Skyrmion configurations.

Findings

Identification of high-density and low-density Skyrmion phases

Characterization of the phase transition and order parameter behavior

Dependence of Skyrmion solutions on sphere radius and potential

Abstract

We study static solutions of the Skyrme model on the two-sphere of radius L, for various choices of potential. The high-density Skyrmion phase corresponds to the ratio beta=L/(size of Skyrmion) being small, whereas the low-density phase corresponds to beta being large. The transition between these two phases, and in particular the behaviour of a relevant order parameter, is examined.