1991/11/01 by Edward D. Weinberger · 2 citations
Physics and Astronomy · Mathematics · #Theoretical and Computational Physics #Stochastic processes and statistical mechanics #Complex Network Analysis Techniques #Physics #Maxima and minima #Quadratic growth #Hamiltonian (control theory) #Spin glass #Energy landscape #Distribution (mathematics) #Statistical physics #Maxima #Distribution function #Energy (signal processing) #Quantum mechanics #Thermodynamics #Mathematical analysis #Mathematics
paper · doi:10.1103/physreva.44.6399
openalex publication_date 1991/11/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.