On the spin wave problem in the Heisenberg model of Ferromagnetism

Jill C. Bonner, Gerhard H. Muller

The problem of the critical behavior of the spin-1/2 Heisenberg ferromagnetic chain has challenged many research workers since 1964. We discuss the critical exponents α and γ recently determined by Schlottmann and by Takahashi and Yamada in the context of previously known Tc=0 critical properties of the 1D s=1/2 XXZ model and the classical Heisenberg model, and we comment on the manifest breakdown of scaling in the s=1/2 Heisenberg ferromagnet.

J. Leo van Hemmen, A. A. S. Brito, Walter Felipe Wreszinski

Y. Tsuchida

Problems of the localized spin wave states in a semi-infinite one-dimensional Heisenberg ferromagnet with impurity spins are studied by the scattering matrix method. The rigorous expressions for the energy and the wave function of the localized spin wave state are obtained in the presence of a boundary.

Marvin D. Girardeau

The ground and excited states of a one-dimensional (1D) spin-1/2 Fermi gas (SFG) with both attractive zero-range odd-wave interactions and repulsive zero-range even-wave interactions are mapped exactly to a 1D Lieb-Liniger-Heisenberg (LLH) model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, such that the complete SFG and LLH energy spectra are identical. The ground state in the ferromagnetic phase is given exactly by the Lieb-Liniger (LL) Bethe ansatz, and that in the antiferromagnetic phase by a variational method combining Bethe ansatz solutions of the LL and 1D Heisenberg models. There are excitation branches corresponding to LL type I and II phonons and spin waves, the latter behaving quadratically for small wave numbers in the ferromagnetic phase and linearly in the antiferromagnetic phase.

George Allen Baker Jr., H.E. Gilbert, Jemimah K. Eve +1 more