Discrete energy landscapes and replica symmetry breaking at zero temperature

The order parameter P(q) for disordered systems with degenerate ground stat es 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 z ero-energy large-scale excitations ( complex energy landscape). Such a situ ation should arise in the 3-dimensional +/-J Ising pin glass and in MAX-SAT . Also, we argue that if the energy landscape is complex with a finite numb er of ground-state families, then replica symmetry breaking reappears at po sitive temperature.