Local properties of Kauffman's Nk model: A tunably rugged energy landscape
Abstract
The Nk model is a dilute, kary 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 spinglass 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:
 10.1103/PhysRevA.44.6399
 Bibcode:
 1991PhRvA..44.6399W
 Keywords:

 64.60.Cn;
 87.10.+e;
 Orderdisorder transformations;
 statistical mechanics of model systems;
 General theory and mathematical aspects