New Type of Phase Transition

Abstract

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