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.
Perturbative analysis of disordered ising models close to criticality / Cirillo, Emilio Nicola Maria; BERTINI MALGARINI, Lorenzo; Enzo, Olivieri. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 126:4-5(2007), pp. 987-1006. (Intervento presentato al convegno Conference on Mathematical Physics of Spin Glasses tenutosi a Cortona, ITALY nel 2005) [10.1007/s10955-006-9214-8].
Perturbative analysis of disordered ising models close to criticality
CIRILLO, Emilio Nicola Maria;BERTINI MALGARINI, Lorenzo;
2007
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.
