Gibbs states of continuum particle systems with unbounded spins: Existence and uniqueness
We study an infinite system of particles chaotically distributed over a Euclidean space R-d. Particles are characterized by their positions x is an element of R-d and an internal parameter (spin) sigma(x) is an element of R-m 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. Published by AIP Publishing.
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Amer Inst Physics