Enumeration of States in a Periodic Glass

We present an analytic enumeration of the metastable states, $N_s$, in a periodic long-range Josephson array frustrated by a transverse field. We find that the configurational entropy, $S_{conf} \equiv \ln N_s$, is extensive and scales with frustration, confirming that the non-random system is glassy. We also find that $S_{conf}$ is different from that of its disordered analogue, despite that fact that the two models share the same dynamical equations.