Critical behavior of the disordered three-color Ashkin-Teller Model -- A Monte Carlo study

The impact of quenched disorder on systems undergoing first-order phase transitions has received less attention than its effects on critical points. A notable exception is the seminal work by Aizenmann and Wehr\footnote{M. Aizenman and J. Wehr, PRL 62, 2503 (1989).}. Building on earlier work by Imry, Ma and others, they rigorously proved the vanishing of latent heat in dimensions $d\leq 2$ in the presence of quenched disorder. In this context, we numerically study the critical behavior of a three-color Ashkin Teller (AT) model in the presence of bond randomness. The clean AT model is known to exhibit a fluctuation-driven first-order transition. An analytical renormalization group treatment by Cardy\footnote{J. Cardy, J. Phys. A 29, 1897 (1996).} predicted that disorder rounds this transition and leads to a critical point in the clean Ising universality class. However, recent numerical work\footnote{A. Bellafard et al, PRL 109, 155701 (2012).} has questioned the veracity of these results. We therefore use Monte-Carlo techniques to re-examine the role of quenched disorder on the three-color AT model. We determine the order of the phase transition, and we perform a systematic finite-size scaling analysis of various thermodynamic quantities to extract the critical behavior.