Aperiodicity in equilibrium systems: Between order and disorder

Abstract

Spatial aperiodicity occurs in various models and material s. Although today the most well-known examples occur in the area of quasicrystals, other applications might also be of interest. Here we discuss some issues related to the notion and occurrence of aperiodic order in equilibrium statistical mechanics. In particular, we consider some spectral characterisations,and shortly review what is known about the occurrence of aperiodic order in lattice models at zero and non-zero temperatures. At the end some more speculative connections to the theory of (spin-)glasses are indicated.

Contribution to ICQ12, some corrections and explanatory remarks added

References in corpus (10)

• Pure Point Dynamical and Diffraction Spectra
• Order in glassy systems
• First Order Phase Transition in a Model of Quasicrystals
• Close-packed dimers on the line: diffraction versus dynamical spectrum
• Pure Glass in Finite Dimensions
• Statistical mechanics of glass transition in lattice molecule models
• Entropic commensurate-incommensurate transition
• Absence of singular continuous diffraction for discrete multi-component particle models
• A comment on the relation between diffraction and entropy
• An ultrametric state space with a dense discrete overlap distribution: Paperfolding sequences