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We study the critical behavior of the 2D $N$-color Ashkin-Teller model in thepresence 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 differentcolors sitting at the same site are coupled by the same bond and map thisproblem onto the 2D system of $N/2$ flavors of interacting Dirac fermions inthe presence of correlated disorder. Using renormalization group we show thatfor $N=2$, a "weakly universal" scaling behavior at the continuous transitionbecomes universal with new critical exponents. For $N>2$, the first-order phasetransition is rounded by the correlated disorder and turns into a continuousone.

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