Perturbative analysis of disordered Ising models close to criticality
Disordered Systems and Neural Networks
2015-05-30 v1 Mathematical Physics
math.MP
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 tools in the proof are a general theory of graded cluster expansions and a stochastic domination of the disorder.
Keywords
Cite
@article{arxiv.1110.5798,
title = {Perturbative analysis of disordered Ising models close to criticality},
author = {L. Bertini and Emilio N. M. Cirillo and E. Olivieri},
journal= {arXiv preprint arXiv:1110.5798},
year = {2015}
}