2005/12/31 by Z. Burda, A. Krzywicki, Olivier Martin +3
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Theoretical and Computational Physics #Topological and Geometric Data Analysis #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.73.036110
published as Phys. Rev. E 73, 036110 (2006) · 10 pages, 9 figs, slightly improved presentation, more references, accepted for publication in Phys Rev E
arxiv created 2006/02/07 · openalex publication_date 2006/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy function, we investigate the properties of the energy landscape for a variety of graph topologies. First, we find that the multiplicity N(s) of the inherent structures generically has a log-normal distribution. In addition, the large volume limit of ln <N(s)>/<ln N(s)> differs from unity, except for the Sherrington-Kirkpatrick model. Second, we find simple scaling laws for the growth of the height of the energy barrier between the two degenerate ground states and the size of the associated valleys. For finite connectivity models, changing the topology of the underlying graph does not modify qualitatively the energy landscape, but at the quantitative level the models can differ substantially.