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We study an infinite system of particles chaotically distributed over a Euclidean space R d . Particles are characterized by their positions x ∈ R d and an internal parameter (spin) σx ∈ 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. Thedoi:10.1063/1.5021464 fatcat:5yoixxza4zcutakxrlb46wocte