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This transition persists for small, nonzero, fixed temperatures and broadens at larger temperatures.
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The position of the transition also depends on the length of time that we allow the algonthm to run. In all of our numerical experiments, we waited sufficiently long that further increases in running time did not noticeably affect the transition.
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Without interaction (K = 0), there will be no transition; this effect persists up to some nonzero degree of interaction (Fig. 1). It requires a sufficient amount of conflict between variables to overcompensate for the downward trend in energy obtained by accepting (in parallel) only spin flips that individually lower the energy
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5644231416
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We thank D Stein for helpful discussions, and H. Abelson, G J Sussman, J. Tsitsiklis, E. Hung, N. Berker, E Todorov, J. Tenenbaum, A. Khwaja, P. Beebee, and the reviewers for useful suggestions. This work was partially supported by Advanced Research Projects Agency grant ARPA ONR-N00014-92-J-4097 and National Science Foundation grant NSF MIP-9001651 (A.G S ), and by Department of Energy grant DOE DE-FG03-93-ER61639, NSF BIR-9218746, and National Institutes of Health grant 5-R01 GM49619 (W G M and S.A K.).
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