On the number of infinite geodesics and ground states in disordered systems

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9 Scopus citations

Abstract

We study first-passage percolation models and their higher dimensional analogs - models of surfaces with random weights. We prove that under very general conditions the number of lines or, in the second case, hypersurfaces which locally minimize the sum of the random weights is with probability one equal to 0 or with probability one equal to + ∞. As corollaries we show that in any dimension d ≥ 2 the number of ground states of an Ising ferromagnet with random coupling constants equals (with probability one) 2 or + ∞. Proofs employ simple large-deviation estimates and ergodic arguments.

Original languageEnglish (US)
Pages (from-to)439-447
Number of pages9
JournalJournal of Statistical Physics
Volume87
Issue number1-2
DOIs
StatePublished - Apr 1997

Keywords

  • Disordered systems
  • First-passage percolation
  • Geodesics
  • Ground states
  • Large deviations
  • Minimal hypersurfaces

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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