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Random and ordered phases of off-lattice rhombus tiles | | Stephen Whitelam
; Isaac Tamblyn
; Peter H. Beton
; Juan P. Garrahan
; | | Date: |
7 Sep 2011 | | Abstract: | We study the covering of the plane by non-overlapping rhombus tiles. This
problem is well-studied only in the limiting case of regular rhombi constrained
by an underlying lattice (equivalent to the problem of dimer coverings of
regular lattices). Here 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 solidification
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. We predict
novel behaviors that might be realized through the self-assembly of ’molecular
rhombi’. | | Source: | arXiv, 1109.1450 | | Services: | Forum | Review | PDF | Favorites | |
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