Random and ordered phases of off-lattice rhombus tiles

Details Random and ordered phases of off-lattice rhombus tiles Random and ordered phases of off-lattice rhombus tiles

2011-09-07

arxiv.org/abs/1109.1450v2

Phys. Rev. Lett. 108, 035702 (2012)

Physics

Condensed Matter

Statistical Mechanics

Supp. Info. and version with high-res figures at http://nanotheory.lbl.gov/people/rhombus_paper/rhombus.html

Scientific paper

10.1103/PhysRevLett.108.035702

We study the covering of the plane by non-overlapping rhombus tiles, a problem well-studied only in the limiting case of dimer coverings of regular lattices. We go beyond this limit by allowing tiles to take any position and orientation on the plane, to be of irregular shape, and to possess different types of attractive interactions. Using extensive numerical simulations we show that at large tile densities there is a phase transition from a fluid of rhombus tiles to a solid packing with broken rotational symmetry. We observe self-assembly of broken-symmetry phases, even at low densities, in the presence of attractive tile-tile interactions. Depending on tile shape and interactions the solid phase can be random, possessing critical orientational fluctuations, or crystalline. Our results suggest strategies for controlling tiling order in experiments involving `molecular rhombi'.

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