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The phase transition phenomenon is one of the central problems of statisticalmechanics. It occurs when the model possesses multiple Gibbs measures. In thispaper, 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 functionalequation, which each solution of the equation corresponds to a Gibbs measure.We give some sufficiency conditions on the existence of multiple Gibbs measuresfor the model. We give a review of some known (translation-invariant, periodic,non-periodic) Gibbs measures of the model and compare them with our newmeasures. We show that the Gibbs measures found in the paper differ from theknown Gibbs measures, i.e, we show that these measures are new.

A new set of Gibbs measures for the SOS model on a Cayley tree