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

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

2007-07-13

arxiv.org/abs/0707.1965v2

Phys. Rev. E 76, 051107 (2007).

Physics

Condensed Matter

Disordered Systems and Neural Networks

minor changes and references added

Scientific paper

10.1103/PhysRevE.76.051107

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, for spin glasses based on random graphs, the degree distribution of the network of inherent structures exhibits a non-trivial scale-free tail.

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