Journal of Statistical Physics

, Volume 126, Issue 4–5, pp 987–1006 | Cite as

Perturbative Analysis of Disordered Ising Models Close to Criticality

  • Lorenzo Bertini
  • Emilio N. M. Cirillo
  • Enzo Olivieri


We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor ferromagnetic couplings and no external magnetic field. We show that, if the probability of supercritical couplings is small enough, the system admits a convergent cluster expansion with probability one. The associated polymers are defined on a sequence of increasing scales; in particular the convergence of the above expansion is compatible with the infinite differentiability of the free energy but does not imply its analyticity. The basic tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder.


ising models disordered systems cluster expansion griffiths’ singularity 


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Lorenzo Bertini
    • 1
  • Emilio N. M. Cirillo
    • 2
  • Enzo Olivieri
    • 3
  1. 1.Dipartimento di MatematicaUniversità di Roma La Sapienza Piazzale Aldo Moro 2RomaItaly
  2. 2.Dipartimento Me. Mo. Mat.Università di Roma La SapienzaRomaItaly
  3. 3.Dipartimento di MatematicaUniversità di Roma Tor VergataRomaItaly

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