"valley Structures" in the Phase Space of a Nite 3d Ising Spin Glass with I Inter- Actions

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 non-linear discrete optimization "valley struc-tures" in the phase space can be analysed for nite systems. The existence of nontrivial breaking of ergodicity at zero temperature is shown by arranging the highly degenerated ground states in several valleys, which are connected only by the excited states. The strange structure of the phase space seems to be related with the unusual behaviour of spin glasses. But up to now, there is no detailed knowledge concerning this structure. It was found that the geometry of the space of equilibrium states has a special hierarchical topology characterized by ultrametricity 1] and by bifurcation-like splitting 2]. A complex spanning phase-space structure is suggested by the method of damage spreading 3] analogous to a percolating cluster in a high-dimensional hyper cube 4]. There is evidence for nontrivial breaking of ergodicity at zero temperature 5]. Because of the high dimension of phase space and the non polynomial effort in nding ground states and excitations of spin-glass models a detailed analysis is very diicult. For two-dimensional spin-glass systems without external eld the ground states are found either by exact minimisation for small lattice sizes in polynomially increasing computing time 6, 7, 8] or by 1