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Random and ordered phases of off-lattice rhombus tiles
S. Whitelam, I. Tamblyn, P.H. Beton and J.P. Garrahan Physical Review Letters, 108, 035702 (2012) This study uses numerical simulations to investigate the self-assembly of non-overlapping rhombus tiles that can adopt any position and orientation on the plane, possess irregular shapes, and have different types of attractive interactions. The simulations reveal that at high tile densities, the system undergoes a phase transition from a fluid of rhombus tiles to a solid packing with broken rotational symmetry. The work demonstrates that the resulting solid phases can exhibit qualitatively different structural properties depending on the specific conditions, moving beyond traditional lattice-based dimer covering problems by introducing greater geometric flexibility. The findings suggest strategies for controlling tiling order in experiments involving molecular rhombi on surfaces. |
