an:03917419
Zbl 0574.60098
Fr??hlich, J??rg; Imbrie, John Z.
Improved perturbation expansion for disordered systems: Beating Griffiths singularities
EN
Commun. Math. Phys. 96, 145-180 (1984).
00150863
1984
j
60K35 82B05
exponential clustering; disordered systems; Griffiths type singularities; large-field problem in real-space renormalization group schemes
We introduce a new expansion to prove exponential clustering of connected correlations in a large class of disordered systems. Our expansion converges for values of the temperature and magnetic field where standard cluster expansions diverge, due to the presence of Griffiths type singularities. It is organized inductively over an infinite sequence of increasing distance scales. In each induction step one redefines what is meant by the ''unperturbed system'', a procedure somewhat reminiscent of K.A.M. theory. Our techniques may be useful in dealing with the so-called large-field problem in real-space renormalization group schemes.