Peculiarities in the density of states of ferromagnetic lattices. Symmetry and instability

A new method is proposed for calculating the density of states of one-magnon excitations in ferromagnetic lattices. It is shown that the singularities in g(ε) correspond to changes in the topology of projections of constant-energy surfaces. A classification of all peculiarities is carried out. The cases when an arbitrary small interaction of next nearest neighbors leads to a strong change in g(ε) are investigated.

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