  The phase transition phenomenon is one of the central problems of statistical
mechanics. It occurs when the model possesses multiple Gibbs measures. In this
paper, we consider a three-state SOS (solid-on-solid) model on a Cayley tree.
We reduce description of Gibbs measures to solving of a non-linear functional
equation, which each solution of the equation corresponds to a Gibbs measure.
We give some sufficiency conditions on the existence of multiple Gibbs measures
for the model. We give a review of some known (translation-invariant, periodic,
non-periodic) Gibbs measures of the model and compare them with our new
measures. We show that the Gibbs measures found in the paper differ from the
known Gibbs measures, i.e, we show that these measures are new.
