Local properties of Kauffman's N-k model: A tunably rugged energy landscape (original) (raw)
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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.
Publication:
Physical Review A
Pub Date:
November 1991
DOI:
Bibcode:
Keywords:
- 64.60.Cn;
- 87.10.+e;
- Order-disorder transformations;
- statistical mechanics of model systems;
- General theory and mathematical aspects