  We define a strict deformation quantization which is compatible with any
Hamiltonian with local spin interaction (e.g. the Heisenberg Hamiltonian) for a
spin chain. This is a generalization of previous results known for mean-field
theories. The main idea is to study the asymptotic properties of a suitably
defined algebra of sequences invariant under the group generated by a cyclic
permutation. Our point of view is similar to the one adopted by Landsman,
Moretti and van de Ven, who considered a strict deformation quantization for
the case of mean-field theories. However, the methods for a local spin
interaction are considerably more involved, due to the presence of a strictly
smaller symmetry group.
