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On metastable configurations of small-world networks

R. Heylen·N. S. Skantzos·J. Busquets Blanco·D. Bolle
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Abstract

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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R. Heylen, N. S. Skantzos, J. Busquets Blanco, D. Bolle. 2005-10-18. On metastable configurations of small-world networks. https://doi.org/10.1103/physreve.73.016138

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