- 96-82 Barata J. C. A. , Marchetti D. H. U.
- Griffiths' Singularities in Diluted Ising Models on the Cayley Tree
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.