On metastable configurations of small-world networks

Details On metastable configurations of small-world networks On metastable configurations of small-world networks

2005-10-18

arxiv.org/abs/cond-mat/0510455v1

Phys. Rev. E 73, 016138 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 4 eps figures

Scientific paper

10.1103/PhysRevE.73.016138

We calculate the number of metastable configurations of Ising small-world networks which are constructed upon superimposing sparse Poisson random graphs onto a one-dimensional chain. Our solution is based on replicated transfer-matrix techniques. We examine the denegeracy of the ground state and we find a jump in the entropy of metastable configurations exactly at the crossover between the small-world and the Poisson random graph structures. We also examine the difference in entropy between metastable and all possible configurations, for both ferromagnetic and bond-disordered long-range couplings.

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