Bethe ansatz for two-magnon scattering states in 2D and 3D Heisenberg–Ising ferromagnets†Dedicated to the memory of L D Faddeev. (26th April 2018)

• Record Type: Journal Article
• Authors: Bibikov, P N
• Is Part Of: Journal of statistical mechanics. (2018:Apr.)
• Publication Date: 2018-04-26
• Subjects: 1 -- 2; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aab84e
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: Two different versions of Bethe ansatz are suggested for evaluation of scattering two-magnon states in 2D and 3D Heisenberg–Ising ferromagnets on square and simple cubic lattices. It is shown that the two-magnon sector is subdivided on two subsectors related to non-interacting and scattering magnons. The former subsector possess an integrable regular dynamics and may be described by a natural modification of the usual Bethe Ansatz. The latter one is characterized by a non-integrable chaotic dynamics and may be treated only within discrete degenerative version of Bethe Ansatz previously suggested by the author. Some of these results are generalized for multi-magnon states of the Heisenberg–Ising ferromagnet on a D dimensional hyper cubic lattice.