Metastable configurations of small-world networks.
We calculate the number of metastable configurations of Ising small-world networks that 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 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.
Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. rob.heylen@fys.kuleuven.be
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