Comparing Extremal and Hysteretic Optimization in Spin Glasses*

We compare the capabilities of the $HO$\footnote{PRL 89, 150201} and the $EO$\footnote{PRL 86, 5211} heuristic in finding spin glass ground states. Using a one-parameter model recently discussed by Katzgraber and Young \footnote{PRB 67, 134410} that interpolates between the mean-field, infinte-dimensional SK spin glass and the finite-dimensional EA lattice spin glass, we evaluate the heuristics as a function of that parameter. Our results show interesting variations in algorithmic behavior that elucidates their properties. It may also indicate a transition in the physics between high and low-dimensional spin glasses.