Large interacting lattice systems: Gibbs states and phase transitions GAČR 201/09/1931

GAČR 201/09/1931

The aim of the project is to develop several aspects of the theory of Gibbs states and phase transitions of lattice models. Gradient lattice models, where the challenge is to understand the case of non-convex potentials, will be studied by means of multiscale analysis and a refinement of cluster expansions. In particular, we will present a proof of the strict convexity of the free energy and unicity of Gibbs states corresponding to a given tilt/deformation for a class of models at low temperatures. Our preceeding proof of coexistence of two distinct Gibs states with the same tilt will be extended to a bigger class of nonconvex potentials. The results of the statistical analysis for Gibbs random fields as spatial models will be generalized to the corresponding spatio-temporal models. A model selection method based on the penalized pseudo-likelihood will be presented. Stationary states of conservative particle systems and the condensation in multiple-jump zero range processes for models of a traffic jam will be studied. The influence of the underlying lattice on interacting particle systems will be investigated. In particular, we will study survival of the contact process on the hierarchical group and on nonamenable lattices, the rebellious voter model on "exotic" lattices, and we will analyse how the proof of phase transitions of lattice models with entropic barrier depends on the considered lattice.