Discrete Skyrmions in 2+1 and 3+1 Dimensions

TL;DR

This paper introduces a lattice-based Skyrme model in 2+1 and 3+1 dimensions, demonstrating that discrete skyrmions are highly stable, akin to their continuum versions, through a consistent discretization approach.

Contribution

It presents a novel lattice formulation of the Skyrme model derived from a consistent radial discretization, analyzing the stability of skyrmions in discrete settings.

Findings

Discrete skyrmions exhibit high stability.

The lattice model closely approximates continuum skyrmions.

Stable solutions exist in both 2+1 and 3+1 dimensions.

Abstract

This paper describes a lattice version of the Skyrme model in 2+1 and 3+1 dimensions. The discrete model is derived from a consistent discretization of the radial continuum problem. Subsequently, the existence and stability of the skyrmion solutions existing on the lattice are investigated. One consequence of the proposed models is that the corresponding discrete skyrmions have a high degree of stability, similar to their continuum counterparts.