  We have previously studied properties of a one-dimensional potential with $N$
equally spaced identical barriers in a (fixed) finite interval for both finite
and infinite $N$. It was observed that scattering and spectral properties
depend sensitively on the ratio $c$ of spacing to width of the barriers (even
in the limit $N \to \infty$). We compute here the specific heat of an ensemble
of such systems and show that there is critical dependence on this parameter,
as well as on the temperature, strongly suggestive of phase transitions.
