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We provide a rigorous calculation of the free energy of a non-metalliccrystal containing a small concentration of defects. The low-temperatureleading contribution is found to be $\propto T^2$. This further gives alinear-in-$T$ low-temperature specific heat as that exhibited by glasses. Theseresults also show that, similarly to what happens in glasses, thelong-wavelength spectrum of a nearly perfect crystal does not suffice todetermine its low-temperature behavior.

A glass-like behavior in the low-temperature specific heat is a natural property of any real crystal