Network of inherent structures in spin glasses: scaling and scale-free distributions

Z. Burda 1, A. Krzywicki 2, O. C. Martin 3

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 76 (2007) 051107

The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest descent dynamics, determining for each disorder sample the transition links appearing within a given barrier height. We find that differences between linked inherent structures are typically associated with local clusters of spins; we interpret this within a framework based on droplets in which the characteristic ``length scale'' grows with the barrier height. We also consider the network connectivity and the degrees of its nodes. Interestingly, when the spin glass is of the mean-field type, the degree distribution of the network of inherent structures exhibits a non-trivial scale-free behavior.

  • 1. Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center,
    Jagellonian University
  • 2. Laboratoire de Physique Théorique d'Orsay (LPT),
    CNRS : UMR8627 – Université Paris XI - Paris Sud
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud