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Quantum Stability for the Heisenberg Ferromagnet

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Bargheer,  Till
Duality & Integrable Structures, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Beisert,  Niklas
Duality & Integrable Structures, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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njp8_10_103023.pdf
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Citation

Bargheer, T., Beisert, N., & Gromov, N. (2008). Quantum Stability for the Heisenberg Ferromagnet. New Journal of Physics, 10: 103023. doi:10.1088/1367-2630/10/10/103023.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-1377-8
Abstract
Highly spinning classical strings on RxS^3 are described by the Landau-Lifshitz model or equivalently by the Heisenberg ferromagnet in the thermodynamic limit. The spectrum of this model can be given in terms of spectral curves. However, it is a priori not clear whether any given admissible spectral curve can actually be realised as a solution to the discrete Bethe equations, a property which can be referred to as stability. In order to study the issue of stability, we find and explore the general two-cut solution or elliptic curve. It turns out that the moduli space of this elliptic curve shows a surprisingly rich structure. We present the various cases with illustrations and thus gain some insight into the features of multi-cut solutions. It appears that all admissible spectral curves are indeed stable if the branch cuts are positioned in a suitable, non-trivial fashion.