Felix Flicker

Rudolf Peierls Centre for Theoretical Physics, University of Oxford Rudolf Peierls Centre for Theoretical Physics, University of Oxford

Classical Dimers on Penrose Tilings

Mathematical Physics Seminar

10th January 2020, 2:00 pm – 3:00 pm
Fry Building, 4th Floor Seminar Room

We study the classical dimer model on rhombic Penrose tilings, whose edges and vertices may be identified with those of a bipartite graph. We find that Penrose tilings do not admit perfect matchings (dimer coverings free of unmatched vertices, or 'monomer' defects). Instead, their maximum matchings (with the fewest monomers) have a monomer density of 81-50*(the golden ratio), approximately 0.098, in the thermodynamic limit. Such matchings divide the tiling into a fractal of nested closed regions. Turning to related structures, we show that dart-kite Penrose tilings instead feature an imbalance of charge between bipartite sub-lattices, leading to a minimum monomer density of (7-4*(the golden ratio))/5, around 0.106, all of one charge. With summer student Jerome Lloyd we show that the Ammann-Beenker tiling admits perfect matchings. We find various other phenomena in dimer models on other quasicrystals.

F. Flicker, S. H. Simon, and S. A. Parameswaran, arXiv 1902.02799

Organiser: Thomas Bothner

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