title: Emergence of limit-periodic order in tiling models.
abstract: A two-dimensional (2D) lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar monotile is known to have a limit-periodic 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 next-nearest-neighbor interactions and introduce closely related 3D models with only nearest-neighbor interactions that exhibit limit-periodic phases. For models with no next-nearest-neighbor interactions of the Taylor-Socolar type, there is a large degenerate class of ground states, including crystalline patterns and limit-periodic ones, but a slow quench still yields the limit-periodic state. For the Taylor-Socolar 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 nearest-neighbor matching rules.
authors.affiliation: Physics Department, Duke University, Durham, North Carolina 27708, USA.
authors.forename: Catherine
authors.initials: C
authors.lastname: Marcoux
authors.affiliation: 726 W Main St., Madison, Wisconsin 53715, USA.
authors.forename: Travis W
authors.initials: TW
authors.lastname: Byington
authors.affiliation: University of Chicago Booth School of Business, 5807 S. Woodlawn Avenue, Chicago, Illinois 60637, USA.
authors.forename: Zongjin
authors.initials: Z
authors.lastname: Qian
authors.affiliation: Chemistry Department, Duke University, Durham, North Carolina 27708, USA and Physics Department, Duke University, Durham, North Carolina 27708, USA.
authors.forename: Patrick
authors.initials: P
authors.lastname: Charbonneau
authors.affiliation: Physics Department, Duke University, Durham, North Carolina 27708, USA.
authors.forename: Joshua E S
authors.initials: JE
authors.lastname: Socolar
mesh_terms: D007700:Kinetics; D008958:Models, Molecular; D008968:Molecular Conformation; D009010:Monte Carlo Method; D044367:Phase Transition; D013816:Thermodynamics