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.
Bertini, L., Cirillo, E., Olivieri, E. (2007). Perturbative analysis of disordered ising models close to criticality. In Journal of Statistical Physics (pp.987-1006). NEW YORK : SPRINGER/PLENUM PUBLISHERS [10.1007/s10955-006-9214-8].
Perturbative analysis of disordered ising models close to criticality
OLIVIERI, ENZO
2007-01-01
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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
