Abstract
Dynamical correlation functions at low temperature for one-dimensional systems that involve the decay of a single elementary excitation into three others show logarithmic singularities at the frequency of the original excitation, as well as discontinuities that become sharper as the temperature is lowered. The discontinuities are the result of an elementary catastrophe that occurs as the phase space available for the decay varies with frequency. They should be observable, for instance, as dramatic changes in the out-of-plane spin-wave linewidth in CsNi${\mathrm{F}}_{3}$ as a function of temperature and wave vector.
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