# Do Goldstone modes with linear dispersion always correspond to superfluidity?

For a superfluid, we get that the Goldstone modes has a linear dispersion. $$\omega=vk$$ where $$v$$ will be a critical velocity. We can have no excitations caused by impurities with a velocity less that the critical one.

This argument seems to hold for all Goldstone modes with a linear dispersion, is it then the case that for linear Goldstone modes imply a superfluid behaviour?