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

Abstract

The work is devoted to gradient Gibbs measures (GGMs) of a SOS model with countable set Z of spin values and having alternating magnetism on Cayley trees. This model is defined by a nearest-neighbor gradient interaction potential. Using Külske-Schriever argument, based on boundary law equations, we give several q-heightperiodic translations invariant GGMs for q = 2, 3, 4.