  We consider the zero-temperature dynamics for the infinite-range, non
translation invariant one-dimensional spin model introduced by Marinari, Parisi
and Ritort to generate glassy behaviour out of a deterministic interaction. It
is shown that there can be a large number of metatastable (i.e., one-flip
stable) states with very small overlap with the ground state but very close in
energy to it, and that their total number increases exponentially with the size
of the system.
