Extremal Optimization (EO), a new local search heuristic, is used to
approximate ground states of the mean-field spin glass model introduced by
Sherrington and Kirkpatrick. The implementation extends the applicability of EO
to systems with highly connected variables. Approximate ground states of
sufficient accuracy and with statistical significance are obtained for systems
with more than N=1000 variables using ±J bonds. The data reproduces the
well-known Parisi solution for the average ground state energy of the model to
about 0.01%, providing a high degree of confidence in the heuristic. The
results support to less than 1% accuracy rational values of ω=2/3 for
the finite-size correction exponent, and of ρ=3/4 for the fluctuation
exponent of the ground state energies, neither one of which has been obtained
analytically yet. The probability density function for ground state energies is
highly skewed and identical within numerical error to the one found for
Gaussian bonds. But comparison with infinite-range models of finite
connectivity shows that the skewness is connectivity-dependent.Comment: Substantially revised, several new results, 5 pages, 6 eps figures
included, (see http://www.physics.emory.edu/faculty/boettcher/ for related
information