Translation-Invariant Gibbs Measures for the Blum-Kapel Model on a Cayley Tree

摘要

In the paper, translation-invariant Gibbs measures for the Blum–Kapelmodel on a Cayley tree of order k are considered. An approximate criticaltemperature Tcr is found such that for T ≥ Tcr there exists a uniquetranslation-invariant Gibbs measure and for 0 T Tcr there are exactlythree translation-invariant Gibbs measures. In addition, the problem of(not) extremality for the unique Gibbs measure is studied.