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 (Külske et al., J Stat Phys 156 (2014), 189–200) we gave a full description of the TISGMs, and showed in particular that at sufficiently low temperatures their number is . 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 extremal TISGMs. For the Cayley tree of order two we give explicit formulae and some numerical values. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 636–678, 2017