非周期、拓扑及非关联无序下干净临界点稳定性的数值研究

中文摘要 AI 辅助

利用二维Ashkin-Teller（AT）模型，我们比较了三种非周期晶格上的临界行为：Smith-hat非周期平铺、Voronoi-Delaunay（VD）随机三角剖分以及非关联稀释方格。块平均配位涨落$σ_Q$随指数$α$的衰减被用来描述连通性无序。前两种晶格具有相同的指数$α$，与第三种不同。我们考虑相关长度指数$ν<1$的区域，此时根据Harris判据$d ν\le 2$，随机性是相关的，但根据Harris--Barghathi--Vojta（HBV）判据，在$αν>1$的Smith-hat平铺和VD三角剖分情况下，随机性应是不相关的。对于稀释晶格，我们确实发现干净普适行为沿整个临界线被破坏，表明交叉到由无序主导的固定线，这与Harris判据和HBV判据一致。相反，VD和Smith-hat晶格均展现出与干净AT普适类一致的临界指数，并通过Coulomb-gas自洽性检验验证，这违反了Harris判据但符合HBV判据。

英文摘要

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.

发表机构

• School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）
• Key Laboratory of Multiscale Spin Physics (Beijing Normal University), Ministry of Education（教育部多尺度自旋物理重点实验室（北京师范大学））
• School of Physics, Beijing Institute of Technology（北京理工大学物理学院）

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11 pages, 11 figures