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Gibbs states of continuum particle systems with unbounded spins: existence and uniqueness

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JournalJournal of Mathematical Physics
DateAccepted/In press - 4 Jan 2018
DatePublished (current) - 24 Jan 2018
Issue number1
Volume59
Number of pages25
Original languageEnglish

Abstract

We study an infinite system of particles chaotically distributed over a Euclidean space Rd. Particles are characterized by their positions x∈Rd and an internal parameter (spin) σx∈Rm and interact via position-position and (position dependent) spin-spin pair potentials. Equilibrium states of such system are described by Gibbs measures on a marked configuration space. Due to the presence of unbounded spins, the model does not fit the classical (super-) stability theory of Ruelle. The main result of the paper is the derivation of sufficient conditions of the existence and uniqueness of the corresponding Gibbs measures.

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