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We investigate classical Heisenberg models with the translation symmetries ofinfinite crystals. We prove a spiral theorem, which states that under certainconditions there must exist spiral ground states, and propose a naturalclassification of all manageable models based on some "spectral properties,"which are directly related to their ground state manifolds. We demonstrate howthe ground state manifold can be calculated analytically for all spectra withfinite number of minima and some with extensive minima, and algorithmically forthe others. We also extend the method to particular anisotropic interactions.

General method for finding ground state manifold of classical Heisenberg model