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

Diana Conache, Alexei Daletskii, Y. Kondratiev, Tanja Pasurek

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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.

Original languageEnglish
Article number013507
Number of pages25
JournalJournal of Mathematical Physics
Issue number1
Publication statusPublished - 24 Jan 2018

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