Low-temperature phonon dynamics of a classical compressible Heisenberg chain

A low-temperature calculation of the influence of the anharmonicity of the phonons on the dynamic structure factor is made for a compressible Heisenberg system. The anharmonicity is caused by the coupling of phonons and spins. The memory function of the displacement relaxation function is calculated to lowest order in the temperature. Only two-magnon processes are found to contribute to the memory function in this limit. The displacement relaxation function turns out to be very simple. The collision processes can lead to a second resonance. In two limits, the results are compared with the results of a continued fraction approximation. The qualitative agreement is good