Integration of the stationary problem for a classical spin chain

A general solution is found to the stationary problem for an anisotropic discrete Heisenberg chain with classical spins and also its natural generalization - the discrete analog of the n-dimensional Neumann problem. Explicit expressions are obtained for the solutions in terms of theta functions, and also expressions for the energy of these solutions. The integration is based on the interpretation of the solutions in terms of a Bloch eigen-function of a finite-gap different Schroedinger operator