96-82 Barata J. C. A. , Marchetti D. H. U.

Griffiths' Singularities in Diluted Ising Models on the Cayley Tree (433K, Postscript) Mar 19, 96

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Abstract. The Griffiths' singularities are exhibited for a class of diluted ferromagnetic Ising models defined on the Cayley tree (Bethe lattice). For the deterministic model the Lee-Yang circle theorem is explicitly proven for the magnetization at the origin and it is shown that, in the thermodynamic limit, the Lee-Yang singularities become dense in the entire unit circle for the whole ferromagnetic phase. Smoothness (infinite differentiability) of the quenched magnetization $m$ at the origin with respect to the external magnetic field is also proven for convenient choices of temperature and disorder. From our analysis one also concludes that the existence of metastable states is impossible for the random models in consideration.

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