Discrete energy landscapes and replica symmetry breaking at zero temperature

Abstract

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.

7 pages; clarifications on valley definitions

References in corpus (2)

• Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences
• A variational description of the ground state structure in random satisfiability problems

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• Evidence for the double degeneracy of the ground-state in the 3D $\pm J$ spin glass
• Direct sampling of complex landscapes at low temperatures: the three-dimensional +/-J Ising spin glass
• Discreteness and entropic fluctuations in GREM-like systems
• Entropic long range order in a 3D spin glass model
• The discrete random energy model and one step replica symmetry breaking