New Type of Phase Transition

It is shown that the ferromagnetic Ising model on a Cayley tree lattice exhibits a new type of phase transition at the field $B=0$ below the Bethe-Peierls transition temperature TBP. The leading nonanalytic part of the free energy is of the form B^κ, where the "critical" exponent κ(T) increases smoothly from one to infinity as the temperature goes from 0 to TBP. This implies a transition of "continuous" order κ.