Inspired by phason dynamics in tiling models of quasicrystals, we investigate a class of constrained Ising models. Phason shifts in the Penrose tiling model of quasicrystals appear as flips of rows of tiles, known as ‘‘worms.’’ When worms cross one another, a hierarchy is established in which some of the worms cannot flip until others have. A complex set of constraints on worm flips is thereby introduced by the intricate pattern of worm crossings in quasicrystalline tilings. We introduce a simple model of interacting sets of one-dimensional Ising chains that mimics this set of constraints and study the possible consequences of these constraints for phason dynamics and the relaxation of phason strain in quasicrystals.

• Received 4 June 1990

DOI:https://doi.org/10.1103/PhysRevB.42.8517