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

## TL;DR

This paper investigates how correlated disorder affects the critical behavior of the 2D N-color Ashkin-Teller model, revealing universal scaling for N=2 and a disorder-induced transition from first-order to continuous for N>2.

## Contribution

It demonstrates that correlated disorder induces universal critical behavior for N=2 and converts first-order transitions into continuous ones for N>2 in the 2D Ashkin-Teller model.

## Key findings

- For N=2, disorder leads to universal critical exponents.
- For N>2, disorder rounds first-order transitions into continuous ones.
- Correlated disorder significantly alters phase transition nature.

## Abstract

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.