Dynamic phase diagram of the number partitioning problem

Area of Science:

• Statistical Physics
• Computational Physics

Background:

• The number partitioning problem is complex.
• Simple trap models offer insights into dynamics.

Purpose of the Study:

• Investigate the dynamic phase diagram of a spin model related to number partitioning.
• Analyze the influence of simultaneous spin flips on system dynamics.

Main Methods:

• Studied a spin model with varying temperature and fraction of simultaneous spin flips (K/N).
• Mapped K=1 to Bouchaud's trap model and K=N to Barrat-Mézard's entropic trap model.
• Analyzed intermediate cases (1<

Main Results:

• Observed a transition from activated to entropic regimes at T(g)/2.
• Identified ergodicity breaking below T(g)/2 for K/N -> 0.
• Found a non-trivial fluctuation-dissipation relation and a single effective temperature (T(g)/2) for K<

Conclusions:

• The spin model exhibits distinct dynamic regimes based on K/N.
• Results highlight the relevance and limitations of simple trap models for complex systems.