title: Stability of two-dimensional soft quasicrystals in systems with two length scales.
abstract: The relative stability of two-dimensional soft quasicrystals in systems with two length scales is examined using a recently developed projection method, which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal, and octagonal quasicrystals, are obtained for a simple model, i.e., the Lifshitz-Petrich free-energy functional, of soft quasicrystals with two length scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.
authors.affiliation: School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, P.R. China.
authors.forename: Kai
authors.initials: K
authors.lastname: Jiang
authors.affiliation: LMAM, CAPT and School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China.
authors.forename: Jiajun
authors.initials: J
authors.lastname: Tong
authors.affiliation: LMAM, CAPT and School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China.
authors.forename: Pingwen
authors.initials: P
authors.lastname: Zhang
authors.affiliation: Department of Physics & Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1.
authors.forename: An-Chang
authors.initials: AC
authors.lastname: Shi