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 $B=0$ below the Bethe-Peierls transition temperature ${T}_{\mathrm{BP}}$. The leading nonanalytic part of the free energy is of the form ${B}^{\ensuremath{\kappa}}$, where the "critical" exponent $\ensuremath{\kappa}(T)$ increases smoothly from one to infinity as the temperature goes from 0 to ${T}_{\mathrm{BP}}$. This implies a transition of "continuous" order $\ensuremath{\kappa}$.