GIBBS MEASURES FOR THE POTTS-SOS MODEL WITH THREE STATES OF SPIN VALUES

We consider Potts and solid-on-solid model (so called mixed P-SOS model), with spin values which belong to a discrete set such as 0, 1, 2, …, m on an arbitrary branched Cayley tree. For the statement m=2, we obtain a special class of translation-invariant splitting Gibbs measures of the P-SOS model thanks to determining fixed points of a rational function.