Ground-state structure in a highly disordered spin-glass model

C. M. Newman, D. L. Stein

Research output: Contribution to journalArticlepeer-review


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 2script 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 dc = 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 languageEnglish (US)
Pages (from-to)1113-1132
Number of pages20
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - Feb 1996


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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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