
Publications [#248312] of Joshua Socolar
Papers Published
 Marcoux, C; Byington, TW; Qian, Z; Charbonneau, P; Socolar, JES, Emergence of limitperiodic order in tiling models.,
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, vol. 90 no. 1
(July, 2014),
pp. 012136, American Physical Society, ISSN 15393755 [PhysRevE.90.012136], [doi]
(last updated on 2019/06/17)
Abstract: A twodimensional (2D) lattice model defined on a triangular lattice with nearest and nextnearestneighbor interactions based on the TaylorSocolar monotile is known to have a limitperiodic ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. We study the model as a function of the strength of the nextnearestneighbor interactions and introduce closely related 3D models with only nearestneighbor interactions that exhibit limitperiodic phases. For models with no nextnearestneighbor interactions of the TaylorSocolar type, there is a large degenerate class of ground states, including crystalline patterns and limitperiodic ones, but a slow quench still yields the limitperiodic state. For the TaylorSocolar lattic model, we present calculations of the diffraction pattern for a particular decoration of the tile that permits exact expressions for the amplitudes and identify domain walls that slow the relaxation times in the ordered phases. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case, and we include a proof of aperiodicity for a geometrically simple tile with only nearestneighbor matching rules.
