Supersolidity and the Thermodynamics of Solid Helium

The specific heat of solid helium in the temperature range below about 1.2K has been found to contain a term varying as T7, in addition to the usual T3 contribution always found in a crystalline dielectric solid. It has been pro-posed by Anderson, Brinkman and Huse, (Science 310, 1164(2005)) that the existence of this T7 term supports their theory of supersolidity. However, in this paper we show that corrections to the phonon specific heat arising from phonon dispersion are much larger than expected based on simple order of magnitude estimates and, as a consequence, it is very unlikely that the exis-
tence of this T7 term can be considered as evidence for supersolidity.

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