Integration of the stationary problem for a classical spin chain

A general solution of the stationary problem for anisotropic discrete Heisenberg lattice with classical spins and its natural generalization, the discrete version of the classical $n$-dimensional Neumann problem is found. Explicit formulas for solutions in terms of the $\theta$-functions and expressions for energies of these solutions are obtained. Integration is based on the interpretation of the solution in terms of the Bloch eigenfunction of the discrete Schrödinger operator.