Glassy Behavior in the Ferromagnetic Ising Model on a Cayley Tree

Details Glassy Behavior in the Ferromagnetic Ising Model on a Cayley Tree Glassy Behavior in the Ferromagnetic Ising Model on a Cayley Tree

1995-09-07

arxiv.org/abs/cond-mat/9509035v1

Physics

Condensed Matter

32 pages, submitted to J. Phys A, figures available on request

Scientific paper

10.1088/0305-4470/29/18/011

We present a detailed study of the nearest-neighbor ferromagnetic Ising model on a Cayley tree. In the limit of zero field, the system displays glassy behavior 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 number of sites. Non-Gaussian magnetization distributions are observed for $T < T_g$, 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 behavior for a finite but macroscopic number of sites.

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