In the Debye model using BVK boundary conditions, you can't have any phonons with k-vector shorter than 2pi/L but that's generally fine because those states are very low in energy and have low DOS anyways, right
So in the Debye model, is it correct to say that you're basically treating a solid like a continuum but putting a limit on what wavelengths you consider based on the atomic spacing, so that you don't double count equivalent waves?