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Gibbs states on random configurations

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JournalJournal of Mathematical Physics
DatePublished - Aug 2014
Issue number8
Number of pages17
Original languageEnglish


We study a class of Gibbs measures of classical particle spin systems with spin space S=Rm and unbounded pair interaction, living on a metric graph given by a typical realization γ of a random point process in Rn. Under certain conditions of growth of pair- and self-interaction potentials, we prove that the set G(Sγ) of all such Gibbs measures is not empty for almost all γ, and study support properties of νγ∈G(Sγ). Moreover we show the existence of measurable maps (selections) γ↦νγ and derive the corresponding averaged moment estimates.

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