Emergent universal critical behavior of the 2D N-color Ashkin-Teller model in the presence of correlated disorder

We study the critical behavior of the 2D N-color Ashkin-Teller model in the presence of random bond disorder whose correlations decays with the distance r as a power-law r^{-a}. We consider the case when the spins of different colors sitting at the same site are coupled by the same bond and map this problem onto the 2D system of N/2 flavors of interacting Dirac fermions in the presence of correlated disorder. Using renormalization group we show that for N=2, a "weakly universal" scaling behavior at the continuous transition becomes universal with new critical exponents. For N>2, the first-order phase transition is rounded by the correlated disorder and turns into a continuous one