Discrete energy landscapes and replica symmetry breaking at zero temperature

The order parameter P(q) for disordered systems with degenerate ground-states is reconsidered. We propose that entropy fluctuations lead to a trivial P(q) at zero temperature as in the non-degenerate case, even if there are zero-energy large-scale excitations (complex energy landscape). Such a situation should arise in the 3-dimensional ±J Ising spin glass and in MAX-SAT. Also, we argue that if the energy landscape is complex with a finite number of ground-state families, then replica symmetry breaking reappears at positive temperature.