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.
Keywords:
discrete Hamiltonian and contact systems, the Lax representation, complete integrability
Citation:
Jovanović B., Heisenberg Model in Pseudo-Euclidean Spaces, Regular and Chaotic Dynamics,
2014, Volume 19, Number 2,
pp. 245-250