Numerical Study of Stability of Clean Critical Points across Aperiodic, Topological, and Uncorrelated Disorder

Abstract

Using the two-dimensional Ashkin-Teller (AT) model, we compare criticality on three non-periodic lattices: the Smith-hat aperiodic tiling, Voronoi-Delaunay (VD) random triangulations, and uncorrelated diluted square lattices. The decay of the block-averaged coordination fluctuation $\sigma_Q$ with exponent $\alpha$ is used to describe the connectivity disorder. The first two lattices share the same exponent $\alpha$, which differs from that of the third. We consider the regime where the correlation-length exponent $\nu<1$, where randomness is relevant according to the Harris criterion $d \nu \le 2$, but should be irrelevant in cases of the Smith-hat tiling and VD triangulations, where $\alpha \nu>1$, according to the Harris--Barghathi--Vojta (HBV) criterion. For the diluted lattice, we indeed find that the clean universality behavior breaks down along the entire critical line, indicating a crossover to a fixed line dominated by disorder, in line with both the Harris criterion and the HBV criterion. In contrast, both VD and Smith-hat lattices display critical exponents consistent with the clean AT universality class, as validated by a Coulomb-gas self-consistency check, violating the Harris criterion while conforming to the HBV criterion.