  We theoretically investigate the dynamical stability of one-dimensional
fullerene polymers by computing the phonon dispersion relations within the
atomistic approach. We find that only seven models among 54 models proposed
previously [J. Phys. Chem. A 119, 3048 (2015)] are dynamically stable. We show
that the low temperature specific heat of them is proportional to the square
root of the temperature in a wider range of temperature compared to the case of
single-walled carbon nanotubes.
