GROUND-STATE STRUCTURE IN A HIGHLY DISORDERED SPIN-GLASS MODEL

We propose a new Ising spin-glass model on Z(d) of Edwards-Anderson ty pe, but with highly disordered coupling magnitudes, in which a greedy algorithm for producing ground stales is exact. We find that the proce dure for determining (infinite-volume) ground states for this model ca n be related to invasion percolation with the number of ground states identified as 2(N), where N = N(d) is the number of distinct global co mponents in the ''invasion forest.'' We prove that N(d) = infinity if the invasion connectivity function is square summable. We argue that t he critical dimension separating N = 1 and N = infinity is d(c) = 8. W hen N(d)= infinity, we consider free or periodic boundary conditions o n cubes of side length L and show that frustration leads to chaotic L dependence with all pairs of ground states occurring as subsequence li mits. We briefly discuss applications of our results to random walk pr oblems on rugged landscapes.