Elasticity of a one-dimensional tiling model and its implication to the phason elasticity of quasicrystals - art. no. 132205

A one-dimensional tiling model with matching rule energy (antiferromagnetic Ising Hamiltonian) is studied. We present an analytic study of a transitio n from the unlocked phase, where free energy is proportional to the square gradient of the perp-space field [f similar to(partial derivativew)(2)], to the locked phase (f similar to\partial derivativew\) in perp-space elastic ity. The phase diagram and the temperature dependence of the elastic consta nt in the unlocked phase show similarity with the two-dimensional Penrose t iling. The results imply that the unlocking transition of a two-dimensional Penrose tiling model is related to the disordering transition in a one-dim ensional Ising model.