  We consider the deterministic model with glassy behaviour, recently
introduced by Marinari, Parisi and Ritort, with \ha\ $H=\sum_{i,j=1}^N
J_{i,j}\sigma_i\sigma_j$, where $J$ is the discrete sine Fourier transform. The
ground state found by these authors for $N$ odd and $2N+1$ prime is shown to
become asymptotically dege\-ne\-ra\-te when $2N+1$ is a product of odd primes,
and to disappear for $N$ even. This last result is based on the explicit
construction of a set of eigenvectors for $J$, obtained through its formal
identity with the imaginary part of the propagator of the quantized unit
symplectic matrix over the $2$-torus.
