GLASSY BEHAVIOR IN THE FERROMAGNETIC ISING-MODEL ON A CAYLEY TREE

We present a detailed study of the nearest-neighbour ferromagnetic Isi ng model on a Cayley tree. In the limit of zero field, the system disp lays glassy behaviour below a crossover temperature, T-g, that scales inversely with the logarithm of the number of generations; thus T-g is inversely proportional to the logarithm of the logarithm of the numbe r of sites. Non-Gaussian magnetization distributions are observed for T < T-g, reminiscent of that associated with the central spin of the E dwards-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.