2007/07/31 by Heinz Horner, H. Horner · 1 citation
Economics, Econometrics and Finance · Materials Science · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Condensed matter physics #Distribution (mathematics) #Energy landscape #Glass transition #Ground state #Material Dynamics and Properties #Mathematical analysis #Mathematics #Metastability #Monte Carlo method #Nuclear magnetic resonance #Physics #Quantum mechanics #Replica #Spin glass #Statistical physics #Statistics #Theoretical and Computational Physics #Thermodynamics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/e2008-00017-1
Minor changes and journal reference added. 10 pages 6 figures
openalex publication_date 2007/12/01 · arxiv created 2007/12/10 · arxiv updated 2015/03/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.