CORRELATIONS BETWEEN METASTABLE STATES IN SPIN-GLASSES

The distribution of local minima in the energy landscape of the infini te-ranged Ising spin glass is studied by calculation of the average nu mber of pairs of metastable states with fixed overlap and energies. Th e average number forms an upper bound on the typical number. It is kno wn that below a critical energy metastable states are globally (strong ly) correlated. Above the critical energy the upper bound on pairs of metastable states suggests that although metastable states are only lo cally (weakly) correlated, an interesting local structure of the energ y landscape may be present.