  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 for the specific heat and
energy-energy correlations are identical and no logarithmic corrections are
present. The disorder produces a quasi-periodic modulation of the amplitude of
the correlations and a renormalization of the velocities, that is the
coefficients of the rescaling of positions, and of the critical temperature.
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 in both directions and for any
angle. Small divisors are controlled assuming a Diophantine condition on the
frequencies and convergence of the series is proved by Renormalization Group
analysis.
