Liers, Frauke and Palassini, Matteo and Hartmann, Alexander K. and Jünger, Michael (2003) Ground state of the Bethe lattice spin glass and running time of an exact optimization algorithm.
Published in: Physical Review B Vol. 68 (9). 094406.

Abstract

We study the Ising spin glass on random graphs with fixed connectivity z and with a Gaussian distribution of the couplings, with mean mu and unit variance. We compute exact ground states by branch-and-cut with z=4,6 and system sizes up to 1280 spins, for different values of mu . We locate the spin-glass/ferromagnet phase transition Near the phase transition, we observe a sharp change of the median running time of our implementation of the algorithm, consistent with a change from a polynomial dependence on the system size, deep in the ferromagnetic phase, to slower than polynomial in the spin-glass phase.

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