Fuzzy transformations and extremality of Gibbs measures for the Potts   model on a Cayley tree
  We continue our study of the full set of translation-invariant splitting Gibbs measures (TISGMs, translation-invariant tree-indexed Markov chains) for the $q$-state Potts model on a Cayley tree. In our previous work \cite{KRK} we gave a full description of the TISGMs, and showed in particular that at sufficiently low temperatures their number is $2^{q}-1$.   In this paper we find some regions for the temperature parameter ensuring that a given TISGM is (non-)extreme in the set of all Gibbs measures.   In particular we show the existence of a temperature interval for which there are at least $2^{q-1} + q$ extremal TISGMs.   For the Cayley tree of order two we give explicit formulae and some numerical values. 
C. Kuelske, U. A. Rozikov
math-ph math.MP