06-114 L. Bertini, E.N.M. Cirillo, E. Olivieri

Perturbative analysis of disordered Ising models close to criticality (261K, pdf) Apr 12, 06

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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.

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