تقرير
Entropy and chirality in sphinx tilings
| العنوان: | Entropy and chirality in sphinx tilings |
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| المؤلفون: | Huber, Greg, Knecht, Craig, Trump, Walter, Ziff, Robert M. |
| المصدر: | Physical Review Research 6, 013227 (2024) |
| سنة النشر: | 2023 |
| المجموعة: | Condensed Matter |
| مصطلحات موضوعية: | Condensed Matter - Statistical Mechanics, Condensed Matter - Disordered Systems and Neural Networks |
| الوصف: | As a toy model of chiral interactions in crowded spaces, we consider sphinx tilings in finite regions of the triangular lattice. The sphinx tiles, hexiamonds composed of six equilateral triangles in the shape of a stylized sphinx, come in left and right enantiomorphs. Regions scaled up from the unit sphinx by an integer factor ("Sphinx frames") require tiles of both chiral forms to produce tilings, including crystalline, quasicrystalline, and fully disordered tilings. For frames up to order 13, we describe methods that permit exact enumeration and computation of partition functions using "accelerated backtracking," "seam," and "dangler" algorithms. For larger frames, we introduce a Monte Carlo (MC) method to sample typical tilings. Key to the latter is the identification of fundamental shapes (polyads) that admit multiple tilings and which allow a rejection-free MC simulation. Comment: Earlier version was titled "Riddles of Sphinx Tilings." |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevResearch.6.013227 |
| URL الوصول: | http://arxiv.org/abs/2304.14388 |
| رقم الأكسشن: | edsarx.2304.14388 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevResearch.6.013227 |
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