A new method for analysing ground-state landscapes: ballistic search

A 'ballistic-search' algorithm is presented which allows the identification of clusters (or funnels) of ground states in Ising spin glasses even for moderate system sizes. The clusters are defined to be sets of states, which are connected in state-space by chains of zero-energy flips of spins. The technique can also be used to estimate the sizes of such clusters. The performance of the method is tested with respect to different system sizes and choices of parameters. As an application the ground-stare funnel structure of two-dimensional +/-J spin glasses of systems up to size L = 20 is analysed by calculating a huge number of ground states per realization. A T = 0 entropy per spin of so = 0.078(5)k(B) is obtained.