Continuous order phase transitions on a decorated Cayley tree of connectivity two

The treatment of the Ising model on a Cayley tree given by Müller-Hartmann and Zittartz is extended in the case of connectivity two to a decorated tree containing additional bonds with an arbitrary coupling constant. The possibility of phase transitions is investigated and discussed. The positions of the singular surfaces, on which continuous order phase transitions take place, are examined as functions of coupling constants and external fields.