Glassy behaviour in the ferromagnetic Ising model on a Cayley tree

We present a detailed study of the nearest-neighbour ferromagnetic Ising model on a Cayley tree. In the limit of zero field, the system displays glassy behaviour below a crossover temperature, , that scales inversely with the logarithm of the number of generations; thus is inversely proportional to the logarithm of the logarithm of the number of sites. Non-Gaussian magnetization distributions are observed for , reminiscent of that associated with the central spin of the Edwards - Anderson model on the same tree; furthermore, a dynamical study indicates metastability, long relaxation times and ageing consistent with the development of glassy behaviour for a finite but macroscopic number of sites.