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

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.

12 pages + 4 figures, LaTex, to appear in Nonlinearity

References in corpus (3)

• Kink dynamics in a novel discrete sine-Gordon system
• Stable Topological Skyrmions on the 2D Lattice
• Bogomol'nyi Bounds for Two-Dimensional Lattice Systems

Cited by in corpus (8)

• Topological discrete kinks
• Fast and Slow Blowup in the S^2 Sigma Model and (4+1)-Dimensional Yang-Mills Model
• Approximate analytical solutions of the baby Skyrme model
• Discrete Skyrmions in 2+1 and 3+1 Dimensions
• Noncommutative Baby Skyrmions
• Instability of breathers in the topological discrete sine-Gordon system
• Fermion-soliton scattering in a modified ${\mathbb{CP}}^1$ model
• Lattice Three-Dimensional Skyrmions Revisited