Eigenstates and limit cycles in the SK model

Abstract

The authors study the T=0 mean-field equations for infinite-range spin-glass samples of small size by solving exactly the system for different realisations of the coupling constants. They consider both a serial minimisation algorithm, that explores the local minima of the system, and a parallel algorithm, that can also converge to spurious limit-cycle solutions. The cross energy (defined in the paper) plays for the limit cycles the role of the energy for the true solutions, and they then have a way to characterise such spurious solutions (that have been suggested as a possible candidate to the confused state of a realistic memory). In order to substantiate their results, and the large-N extrapolation, they study how some known infinite-N results can be recovered by the knowledge of their small-N results. They also study the basin of attraction of the different kinds of solutions.