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 σQ 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≤ 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.
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BibTeX
@misc{fan2026numerical,
title = {{Numerical Study of Stability of Clean Critical Points across Aperiodic, Topological, and Uncorrelated Disorder}},
author = {Shuhao Fan and Lu Liu and Wenan Guo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17166},
eprint = {2609.17166},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17166},
}
RIS
TY - UNPB
TI - Numerical Study of Stability of Clean Critical Points across Aperiodic, Topological, and Uncorrelated Disorder
AU - Shuhao Fan
AU - Lu Liu
AU - Wenan Guo
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17166
UR - https://arxiv.org/abs/2609.17166
AB - 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≤ 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.
ER -