We apply a recently developed theory of the nonphononic vibrational density of states (DOS) in glasses to investigate the impact of local frozen-in stresses on the low-temperature specific heat. Using a completely harmonic description we show that the hybridization of the local nonphononic vibrational excitations with the waves leads to a low-frequency DOS, in excess to the Debye one, which varies linearly with frequency up to a certain crossover frequency, and then becomes constant. The actual value of the crossover depends of the ratio between the local stresses and the shear modulus. This excess DOS leads to a low-temperature specific heat with an apparent temperature exponent, which is between one and two, as observed experimentally. We discuss how these findings may be utilized for the characterization of glassy materials. We further compare our findings, which only rely on harmonic interactions, with the predictions of other theories, which invoke anharmonic interactions and tunneling for explaining the low-temperature behavior of the specific heat.

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• Continuum mechanics
• Elasticity
• Phonons
• Specific heat