Roughening of two-dimensional quasicrystals: A study on the Penrose tiling

Journal Article · Wed Jul 01 04:00:00 EDT 1992 · Physical Review, B: Condensed Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.46.769· OSTI ID:7276640

Garg, A ^[1]; Shin, M ^[2]; Strandburg, K J ^[3]

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1. Department of Physics and Astronomy ( ) Materials Research Center, Northwestern University, Evanston, Illinois 60208 (United States)
2. Department of Physics and Astronomy ( ) Materials Research Center, Northwestern University, Evanston, Illinois 60208 (United States) Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States)
3. Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208 (United States) Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 (United States)

We explore the roughening transition of a two-dimensional quasicrystal using a transfer-matrix approach. We study a solid-on-solid model on a Penrose tiling, thus retaining full two-dimensional quasiperiodicity. We find that the interface is smooth at low temperatures. It is necessary to compute the transfer matrix over extremely long distances ({similar to}10{sup 20} tile edges) to determine whether the interface is rough. A blocking scheme suggests a roughening temperature {ital T}{sub {ital R}}=0.28{plus minus}0.01 (all temperatures given in units of {ital J}/{ital k}{sub {ital B}}). If a finite nonzero {ital T}{sub {ital R}} does exist, our results show that the roughness exponent must be discontinuous at {ital T}{sub {ital R}}. We also study the model using an approximate mapping to a one-dimensional Schroedinger equation. In this approximation, for {ital T}{approx lt}0.45, the interface appears rough with oscillatory corrections to scaling for a large {ital x} range, and crosses over to a smooth one as {ital x}{r arrow}{infinity}. The crossover region becomes very large for {ital T}{approx gt}0.45, and we cannot say if there exists a finite {ital T}{sub {ital R}}. We compare the two approaches.

• DOE Contract Number: W-31109-ENG-38
• OSTI ID: 7276640
• Journal Information: Physical Review, B: Condensed Matter; (United States), Journal Name: Physical Review, B: Condensed Matter; (United States) Vol. 46:2; ISSN PRBMD; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

665000* -- Physics of Condensed Matter-- (1992-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
INTERFACES
PHASE TRANSFORMATIONS
ROUGHNESS
STRUCTURAL MODELS
SURFACE PROPERTIES
TRANSFER MATRIX METHOD
TWO-DIMENSIONAL CALCULATIONS