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A relation between a class of stationary points of the energy landscape ofcontinuous spin models on a lattice and the configurations of a Ising modeldefined on the same lattice suggests an approximate expression for themicrocanonical density of states. Based on this approximation we conjecturethat if a O(n) model with ferromagnetic interactions on a lattice has a phasetransition, its critical energy density is equal to that of the n = 1 case,i.e., a system of Ising spins with the same interactions. The conjecture holdstrue in the case of long-range interactions. For nearest-neighbor interactions,numerical results are consistent with the conjecture for n=2 and n=3 in threedimensions. For n=2 in two dimensions (XY model) the conjecture yields aprediction for the critical energy of the Berezinskij-Kosterlitz-Thoulesstransition, which would be equal to that of the two-dimensional Ising model. Wediscuss available numerical data in this respect.

On a microcanonical relation between continuous and discrete spin models