Perturbative analysis of disordered Ising models close to criticality

Details Perturbative analysis of disordered Ising models close to criticality Perturbative analysis of disordered Ising models close to criticality

2011-10-26

arxiv.org/abs/1110.5798v1

Journal of Statistical Physics 126, 987-1006, 2007

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

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 tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder.

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