# gst: riddles of the sphinx tilings, when at low temperatures you could find a chiral order.

<< The sphinx tile, a hexiamond composed of six equilateral triangles in the shape of a sphinx, has interesting and complex tiling behavior due to its chirality and asymmetry. >>️

<< for larger frames (AA) introduce a Monte Carlo (MC) method to create randomized tilings. Key to the latter is the identification of fundamental shapes ("polyads") that have multiple tilings and allow a rejection-free MC move once the polyad is identified. >>

AA << also introduce an Ising-like chiral interaction energy between neighboring sphinx tiles and study how the system behaves as a function of temperature; at low temperatures, chiral ordering is found. >>️

Greg Huber, Craig Knecht, Walter Trump, Robert M. Ziff. Riddles of the sphinx tilings. arXiv: 2304.14388v2 [cond-mat.stat-mech]. May 1, 2023.

https://arxiv.org/abs/2304.14388

Also: 'chiral', 'disorder' in https://www.inkgmr.net/kwrds.html

Keywords: gst, sphinx, sphinx tiles, chirality, asymmetry