"Valley structures" in the phase space of a finite 3d ISING spin glass with

Exact results for ground states and low-lying excitations of short-range Ising spin glass systems in three dimensions are presented. Using an exact method of nonlinear discrete optimization "valley structures" in the phase space can be analysed for finite systems. The existence of non-trivial breaking of ergodicity at zero temperature is shown by arranging the highly degenerate ground states in several valleys, which are connected only by the excited states.

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