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

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.