Publication Date
2014
Journal or Book Title
Physica Scripta
Abstract
In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, an 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 perturbation sis 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, especially so in the vicinity of the continuum limit. The corresponding bifurcation diagram is elucidated and a prescription for selecting the branch asymptoting to the well known continuum limit is given. Finally, the robustness of the spectrally stable solutions is corroborated by the virtue of direct numerical simulations.
Pages
17
Volume
90
Recommended Citation
Charalampidis, E. G.; I, T. A.; and Kevrekidis, P. G., "Lattice Three Dimensional Skyrmions Revisited" (2014). Physica Scripta. 1266.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1266
Comments
This is harvested from arXiv. The published version is located at https://arxiv.org/pdf/1411.1313v2.pdf.