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 $σ_Q$ with exponent $α$ is used to describe the connectivity disorder. The first two lattices share the same exponent $α$, which differs from that of the third. We consider the regime where the correlation-length exponent $ν<1$, where randomness is relevant according to the Harris criterion $d ν\le 2$, but should be irrelevant in cases of the Smith-hat tiling and VD triangulations, where $αν>1$, 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.