PUB - Publikationen an der Universität Bielefeld

Gibbs states of a spin system with the single-spin space S = R-m and unbounded pair interactions are studied. The spins are attached to the points of a realization gamma of a random point process in R-n. Under certain conditions on the model parameters we prove that, for almost all gamma, the set G(S-gamma) of all Gibbs states is nonempty and its elements have support properties, explicitly described in the paper. We also show the existence of measurable selections. gamma bar right arrow nu(gamma) is an element of(S-gamma) (random Gibbs measures) and the corresponding averaged moment estimates. (C) 2014 AIP Publishing LLC.