Time Dependent Local Field Distribution and Metastable States in the SK-Spin-Glass

Abstract

Different sets of metastable states can be reached in glassy systems below some transition temperature depending on initial conditions and details of the dynamics. This is investigated for the Sherrington-Kirkpatrick spin glass model with long ranged interactions. In particular, the time dependent local field distribution and energy are calculated for zero temperature. This is done for a system quenched to zero temperature, slow cooling or simulated annealing, a greedy algorithm and repeated tapping. Results are obtained from Monte-Carlo simulations and a Master-Fokker-Planck approach. A comparison with replica symmetry broken theory, evaluated in high orders, shows that the energies obtained via dynamics are higher than the ground state energy of replica theory. Tapping and simulated annealing yield on the other hand results which are very close to the ground state energy. The local field distribution tends to zero for small fields. This is in contrast to the Edwards flat measure hypothesis. The distribution of energies obtained for different tapping strengths does again not follow the canonical form proposed by Edwards.

Minor changes and journal reference added. 10 pages 6 figures

References in corpus (7)

• Low temperature solution of the Sherrington-Kirkpatrick model
• Double Criticality of the Sherrington-Kirkpatrick Model at T=0
• Marginal States in Mean Field Glasses
• Mechanism for the failure of the Edwards hypothesis in the SK spin glass
• Scaling and Renormalization Group in Replica Symmetry Breaking space: Evidence for a simple analytical solution of the SK model at zero temperature
• Free energy landscapes, dynamics and the edge of chaos in mean-field models of spin glasses
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Cited by in corpus (7)

• Marginal Stability in Structural, Spin and Electron Glasses
• Stability at Random Close Packing
• Dynamics and Correlations among Soft Excitations in Marginally Stable Glasses
• Local field distributions in spin glasses
• Quenches in the Sherrington-Kirkpatrick model
• Self-organized critical behavior and marginality in Ising spin glasses
• Dynamics of an Ising Spin Glass on the Bethe Lattice