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, A 1999, 'Bond percolation in frustrated systems', Annals of Probability, vol. 27, no. 4, pp. 1781-1808. https://doi.org/10.1214/aop/1022874815
    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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