 95240 C.M. Newman, D.L. Stein
 Ground State Structure in a Highly Disordered Spin Glass Model
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May 31, 95

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Abstract. We propose a new Ising spin glass model on $Z^d$ of EdwardsAnderson 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 $2^{\cal N}$, where ${\cal N} = {\cal N}(d)$ is the number of
distinct global components in the ``invasion forest''. We prove that ${\cal N}(d) = \infty$ if the invasion connectivity
function is square summable. We argue that the critical dimension
separating ${\cal N} = 1$ and ${\cal N} = \infty$ is $d_c = 8$. When ${\cal N}(d) = \infty$, we consider free
or periodic boundary conditions on cubes of side length $L$ and show that frustration leads
to chaotic $L$ dependence with {\it all} pairs of ground states occuring as
subsequence limits. We briefly discuss applications of our results to
random walk problems on rugged landscapes.
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