Mirror symmetry of height-periodic gradient Gibbs measures of a SOS model on Cayley trees

Abstract

For the solid-on-solid (SOS) model with spin values from the set of all integers on a Cayley tree we give gradient Gibbs measures (GGMs). Such a measure corresponds to a boundary law (which is an infinite-dimensional vector-valued function defined on vertices of the Cayley tree) satisfying an infinite system of functional equations. We give several concrete GGMs of boundary laws which are independent from vertices of the Cayley tree and (as an infinite-dimensional vector) have periodic, (non-)mirror symmetric coordinates.

Gradient Gibbs measures of an SOS model with alternating magnetism on Cayley trees

“…The resulting field is completely characterized by its gradients. These infinite-volume random fields of gradients are called gradient Gibbs measures, or Funaki-Spohn states [5] (for detailed motivations and very recent results see [1], [2], [7] - [12], [17], [18], [20]).…”