Elasticity of a onedimensional tiling model and its implication to the phason elasticity of quasicrystals
Abstract
A onedimensional 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 perpspace field [f~(∂w)^{2}], to the locked phase (f~\∂w\) in perpspace elasticity. The phase diagram and the temperature dependence of the elastic constant in the unlocked phase show similarity with the twodimensional Penrose tiling. The results imply that the unlocking transition of a twodimensional Penrose tiling model is related to the disordering transition in a onedimensional Ising model.
 Publication:

Physical Review B
 Pub Date:
 April 2001
 DOI:
 10.1103/PhysRevB.63.132205
 Bibcode:
 2001PhRvB..63m2205J
 Keywords:

 61.44.Br;
 Quasicrystals