Abstract
The N-k model is a dilute, k-ary spin glass in which the state of each of the N sites is affected by that site and k of its neighbors. As a function of k for large k, we explicitly compute the number of local minima of the Hamiltonian, the distribution of locally minimal energies and the first two moments of that distribution, and a number of statistical properties of ‘‘downhill’’ walks from random starting positions to local optima on these landscapes, including estimates for their length. We suggest some implications of these results for spin-glass physics and for approximating other landscapes that cannot be modeled using more conventional, quadratically coupled spin glasses.
- Received 14 June 1991
DOI:https://doi.org/10.1103/PhysRevA.44.6399
©1991 American Physical Society