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

Research output: Contribution to journalArticle

9 Citations (Scopus)

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
StatePublished - Apr 1997

Fingerprint

Disordered Systems
Geodesic
Ground State
ground state
First-passage Percolation
Ferromagnet
Large Deviations
Ising
Hypersurface
Corollary
High-dimensional
analogs
Analogue
deviation
Minimise
Line
estimates
Model
Estimate

Keywords

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

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

On the number of infinite geodesics and ground states in disordered systems. / Wehr, Jan.

In: Journal of Statistical Physics, Vol. 87, No. 1-2, 04.1997, p. 439-447.

Research output: Contribution to journalArticle

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