L. Bertini, E.N.M. Cirillo, E. Olivieri
Perturbative analysis of disordered Ising models close to criticality
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ABSTRACT.  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 implies the infinite 
differentiability of the free energy but not its analyticity. 
The basic tool in the proof are a general theory of graded cluster expansion and a stochastic domination of the disorder.