Journal of Statistical Physics

, Volume 88, Issue 1–2, pp 231–268 | Cite as

Griffiths' singularities in diluted ising models on the Cayley tree

  • J. C. A. Barata
  • D. H. U. Marchetti
Articles

Abstract

The Griffiths singularities are fully 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 magnetizationm at the origin with respect to the external magnetic field is also proven for convenient choices of temperature and disorder. From our analysis we also conclude that the existence of metastable states is impossible for the random models under consideration.

Key Words

Lee-Yang singularities Griffiths' singularities infinite differentiability metastable states 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • J. C. A. Barata
    • 1
  • D. H. U. Marchetti
    • 1
  1. 1.Instituto de Física, Universidade de São PauloSão PauloBrazil

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