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Heisenberg model in pseudo-Euclidean spaces. (English) Zbl 1335.37045
Summary: We construct analogues of the classical Heisenberg spin chain model (or the discrete Neumann system), on pseudo-spheres and light-like cones in the pseudo-Euclidean spaces and show their complete Hamiltonian integrability. Further, we prove that the Heisenberg model on a light-like cone leads to a new example of the integrable discrete contact system.

MSC:
37J55 Contact systems
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
39A12 Discrete version of topics in analysis
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