Soliton Dynamics in a Novel Discrete O(3) Sigma Model in (2+1) Dimensions

TL;DR

This paper introduces a lattice version of the (2+1)-dimensional O(3) sigma model that preserves topological bounds and enables explicit static soliton construction, revealing their instability through numerical simulations.

Contribution

It presents a novel lattice formulation of the O(3) sigma model that maintains the Bogomol'nyi bound and allows explicit soliton solutions.

Findings

Lattice solitons are unstable under small perturbations.

Soliton size varies linearly with time in simulations.

The model preserves topological energy bounds on the lattice.

Abstract

The O(3) sigma model in two spatial dimensions admits topological (Bogomol'nyi) lower bound on its energy. This paper proposes a lattice version of this system which maintains the Bogomol'nyi bound and allows the explicit construction of static solitons on the lattice. Numerical simulations show that these lattice solitons are unstable undersmall perturbations; in fact, their size changes linearly with time.