## Abstract

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

Original language | English (US) |
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Pages (from-to) | 1113-1132 |

Number of pages | 20 |

Journal | Journal of Statistical Physics |

Volume | 82 |

Issue number | 3-4 |

DOIs | |

State | Published - Feb 1996 |

## Keywords

- Disorder
- Frustration
- Greedy algorithm
- Ground-state multiplicity
- Invasion percolation
- Minimal spanning tree
- Spin glass

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics