Abstract
We propose a new Ising spin-glass model on Zd of Edwards-Anderson type, but with highly disordered coupling magnitudes, in which a greedy algorithm for producing ground states is exact. We find that the procedure for determining (infinite-volume) ground states for this model can be related to invasion percolation with the number of ground states identified as 2N, whereN=N(d) is the number of distinct global components in the “invasion forest.” We prove thatN(d)=∞ if the invasion connectivity function is square summable. We argue that the critical dimension separatingN=1 andN=∞ isd c=8. WhenN(d)=∞, we consider free or periodic boundary conditions on cubes of side lengthL and show that frustration leads to chaoticL dependence withall pairs of ground states occurring as subsequence limits. We briefly discuss applications of our results to random walk problems on rugged landscapes.
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Newman, C.M., Stein, D.L. Ground-state structure in a highly disordered spin-glass model. J Stat Phys 82, 1113–1132 (1996). https://doi.org/10.1007/BF02179805
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DOI: https://doi.org/10.1007/BF02179805