CORRELATIONS BETWEEN METASTABLE STATES IN SPIN-GLASSES

The distribution of local minima in the energy landscape of the infinite-ranged Ising spin glass is studied by calculation of the average number of pairs of metastable states with fixed overlap and energies. The average number forms an upper bound on the typical number. It is known that below a critical energy metastable states are globally (strongly) correlated. Above the critical energy the upper bound on pairs of metastable states suggests that although metastable states are only locally (weakly) correlated, an interesting local structure of the energy landscape may be present.