Equilibrium quasicrystal phase of a Penrose tiling model

Lei Han Tang, Marko V. Jarić

Research output: Contribution to journalArticlepeer-review

74 Citations (Scopus)

Abstract

A two-dimensional rhombus tiling model with a matching-rule-based energy is analyzed using real-space renormalization-group methods and Monte Carlo simulations. The model spans a range from T=0 quasiperiodic crystal (Penrose tiling) to a random-tiling quasicrystal at high temperatures. A heuristic picture for the disordering of the ground-state quasiperiodicity at low temperatures is proposed and corroborated with exact and renormalization-group calculations of the phason elastic energy, which shows a linear dependence on the strain at T=0 but changes to a quadratic behavior at T>0 and sufficiently small strain. This is further supported by the Monte Carlo result that phason fluctuations diverge logarithmically with system size for all T>0, which indicates the presence of quasi-long-range translational order in the system, meaning algebraically decaying correlations. A close connection between the rhombus tiling model and the general surface-roughening phenomena is established. Extension of the results to three dimensions and their possible implication to experimental systems is also addressed.
Original languageEnglish
Pages (from-to)4524-4546
Number of pages23
JournalPhysical Review B
Volume41
Issue number7
DOIs
Publication statusPublished - 1 Mar 1990
Externally publishedYes

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