Gradient Gibbs measures

In the talk we define (gradient) Gibbs measures of physical models with a countable set of spin values. For SOS (solid-on-solid) model, with spin values from the set of all integers, on a Cayley tree we give some gradient Gibbs measures (GGMs) of the model. Such a measure corresponds to a boundary law (a function defined on vertices of Cayley tree) satisfying a functional equation. In the ferromagnetic SOS case we give several concrete GGMs which correspond to periodic boundary laws.