ON THE PURITY OF THE LIMITING GIBBS STATE FOR THE ISING-MODEL ON THE BETHE LATTICE

We give a proof that for the Ising model on the Bethe lattice, the limiting Gibbs state with zero effective field (disordered state) persists to be pure for temperature below the ferromagnetic critical temperature T-c(F) until the critical temperature T-c(SG) of the corresponding spin-glass model. This new proof revises the one proposed earlier.