Phason Elasticity and Ising Models
We illustrate that locking/unlocking transitions between locked (Penrose tiling-like) and unlocked (random tiling-like) phason dynamics for D-dimensional quasicrystals closely relate to the order/disorder transitions for (D-1)-dimensional Ising models. Namely, a hidden Ising-like symmetry in quasicrystals is found. The transition is observed in the ordering/disordering in worms (sheets) for 2D (3D) quasicrystals. In this paper, a finite-temperature phase transition with the 2D Ising critical exponents in 3D icosahedral quasicrystals is demonstrated using Monte Carlo computer simulations. We also propose a new type of quasicrystals called "absolutely locked quasicrystals" in which uniform phason shifts are prohibited.