R. M. Khakimov

Positive Solutions of a Nonlinear System Characterizing Gibbs Measures in Hard-Core SOS Models on Cayley Trees

We study the $$m$$ -state $$p$$ -Solid-on-Solid model with $$p = \infty$$ on Cayley trees of order $$k \geq 2$$ . We derive a system of functional equations whose solutions correspond to (splitting) Gibbs measures for the model. For cases $$m=2,3$$ we identify conditions under wh...