Physical Sciences and Mathematics Commons^™

Lattice Three-Dimensional Skyrmions Revisited, E G. Charalampidis, T A. Ioannidou, Panayotis G. Kevrekidis

Mathematics and Statistics Department Faculty Publication Series

In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, and a stationary point of a particular energy functional. This paper describes lattice analogues of the aforementioned skyrmions, namely a natural way of using the topological properties of the three dimensional continuum Skyrme model to achieve topological stability on the lattice. In particular, using fixed point iterations, numerically exact lattice skyrmions are constructed; and their stability under small perturbations is explored by means of linear stability analysis. While stable branches of such solutions are identified, it is also shown that they possess a particularly delicate bifurcation structure, …