UNIVERSALITY IN THE 2D QUASI-PERIODIC ISING MODEL AND HARRIS-LUCK IRRELEVANCE

Abstract

We prove that in the 2d Ising Model with a weak bidimensional quasi-periodic disorder in the interaction, the critical behavior is the same as in the non-disordered case, that is the critical exponents are identical and no logarithmic corrections are present. The result establishes the validity of the prediction based on the Harris-Luck criterion and it provides the first rigorous proof of universality in the Ising model in presence of quasi-periodic disorder. The proof combines Renormalization Group approaches with direct methods used to deal with small divisors in KAM theory.