Treatment of divergent intensities at Bragg peaks

[kbarros]

Structure factor intensities are expected to diverge for spin wave excitations with vanishing gap. A frequent source of problems is the case where the ground state has a continuous symmetry leading to Goldstone modes. Consider, for example, long wavelength fluctuations in a ferromagnetically ordered Heisenberg model -- the energy cost of these fluctuations is vanishing, so they can become large.

In linear spin wave wave theory, we can handle this by e.g., regularizing the plotted intensities at the $omega \approx 0$ values.

In classical spin dynamics, the practical problem becomes more severe, because the divergent intensities of $S(q,\omega=0)$ get smeared over all $\omega$ at the ordering vector $q$. The origin of the problem seems to be non-periodicity in any long-time trajectory (the final state can deviate macroscopically from the starting state of the trajectory, so it is invalid to impose periodic boundary conditions in time). Fourier transformation of this "step function" leads to severe "ringing" effects (Gibbs oscillations), and hence the introduction of artificial intensities at all time frequencies $\omega$.

One trick that helps a little bit is to discard the imaginary part of the Fourier transform of the spins, which eliminates the step function and leaves only a "kink" singularity. Perhaps there is something more clever? For example, is that a way to artificially impose that the dynamics effectively disallows time evolution of an order parameter with continuous symmetry (e.g., in the Heisenberg model, fix the net magnetization to a given direction).

[kbarros]

It seems like this will be resolved (to the extent possible) with the upcoming refactors to the dynamical correlation measurements.

[kbarros]

This will be addressed one way or the other with https://github.com/SunnySuite/Sunny.jl/issues/218. Closing in favor of that issue.