New phase transitions of the Ising model on Cayley trees

Abstract. We show that the nearest neighbors Ising model on the Cayley tree exhibits new temperature driven phase transitions. These transitions holds at various inverse temperatures different from the critical one. They are depicted by a change in the number of Gibbs states as well as by a drastic change of the behavior of free energies at these new transition points. We also consider the model in presence of an external field and compute the free energies of translation invariant periodic boundary conditions. Mathematics Subject Classifications (2010). 82B26 (primary); 60K35 (sec-ondary