Bond percolation in frustrated systems

E. De Santis, Alberto Gandolfi

Research output: Contribution to journalArticle

Abstract

We study occurrence and properties of percolation of occupied bonds in systems with random interactions and, hence, frustration. We develop a general argument, somewhat like Peierls' argument, by which we show that in ℤd , d ≥ 2, percolation occurs for all possible interactions (provided they are bounded away from zero) if the parameter p ∈ (0, 1), regulating the density of occupied bonds, is high enough. If the interactions are i.i.d. random variables then we determine bounds on the values of p for which percolation occurs for all, almost all but not all almost none but some, or none of the interactions. Motivations of this work come from the rigorous analysis of phase transitions in frustrated statistical mechanics systems.

Original languageEnglish (US)
Pages (from-to)1781-1808
Number of pages28
JournalAnnals of Probability
Volume27
Issue number4
DOIs
StatePublished - Jan 1 1999

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Interaction
Frustration
I.i.d. Random Variables
Statistical Mechanics
Phase Transition
Zero
Statistical mechanics
Phase transition
Random variables

Keywords

  • Frustration
  • Peierls' argument
  • Percolation
  • Spin glasses

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Bond percolation in frustrated systems. / De Santis, E.; Gandolfi, Alberto.

In: Annals of Probability, Vol. 27, No. 4, 01.01.1999, p. 1781-1808.

Research output: Contribution to journalArticle

De Santis, E. ; Gandolfi, Alberto. / Bond percolation in frustrated systems. In: Annals of Probability. 1999 ; Vol. 27, No. 4. pp. 1781-1808.
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