Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2002-12-30
Phys. Rev. B 68, 094406 (2003).
Physics
Condensed Matter
Disordered Systems and Neural Networks
10 pages, RevTex, 10 eps figures. Some changes in the text
Scientific paper
10.1103/PhysRevB.68.094406
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 using a sophisticated branch-and-cut method for z=4,6 and system sizes up to N=1280 for different values of \mu. We locate the spin-glass/ferromagnet phase transition at \mu = 0.77 +/- 0.02 (z=4) and \mu = 0.56 +/- 0.02 (z=6). We also compute the energy and magnetization in the Bethe-Peierls approximation with a stochastic method, and estimate the magnitude of replica symmetry breaking corrections. 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.
Hartmann Alexander K.
Juenger Michael
Liers Frauke
Palassini Matteo
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