Elasticity of a one-dimensional tiling model and its implication to the phason elasticity of quasicrystals
A one-dimensional tiling model with matching rule energy (antiferromagnetic Ising Hamiltonian) is studied. We present an analytic study of a transition from the unlocked phase, where free energy is proportional to the square gradient of the perp-space field [f~(∂w)2], to the locked phase (f~\|∂w\|) in perp-space elasticity. The phase diagram and the temperature dependence of the elastic constant in the unlocked phase show similarity with the two-dimensional Penrose tiling. The results imply that the unlocking transition of a two-dimensional Penrose tiling model is related to the disordering transition in a one-dimensional Ising model.