title: Stability of icosahedral quasicrystals in a simple model with two-length scales.
abstract: The phase behaviour of a free energy functional with two length scales is examined by comparing the free energy of different candidate phases including three-dimensional icosahedral quasicrystals. Accurate free energy of the quasicrystals has been obtained using the recently developed projection method. The results reveal that the icosahedral quasicrystal and body-centred-cubic spherical phase are the stable ordered phases of the model. Furthermore, the difference between the results obtained from the projection method and the one-mode approximation has been analyzed in detail. The present study extends previous results on two-dimensional systems, demonstrating that the interactions between density waves at two length scales can stabilize two- and three-dimensional quasicrystals.
authors.affiliation: School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, People's Republic of China.
authors.forename: Kai
authors.initials: K
authors.lastname: Jiang
authors.forename: Pingwen
authors.initials: P
authors.lastname: Zhang
authors.forename: An-Chang
authors.initials: AC
authors.lastname: Shi