### Abstract

We study vacancy diffusion on the classical triangular-lattice dimer model, subject to the kinetic constraint that dimers can only translate, but not rotate. A single vacancy, i.e., a monomer, in an otherwise fully packed lattice, is always localized in a treelike structure. The distribution of tree sizes is asymptotically exponential and has an average of 8.16±0.01 sites. A connected pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of monomers is anomalous: x 2 ∝ tβ, with β=0.46±0.06. We also find that the same exponent β governs diffusion of clusters of three or four monomers, as well as the diffusion of dimers at finite but low monomer densities. We argue that coordinated motion of monomer pairs is the basic mechanism allowing large-scale transport at low monomer densities. We further identify a "swap-tunneling" mechanism for diffusion of monomer pairs, where a subtle interplay between swap moves (translations of dimers transverse to their axes) and glide moves (translations of dimers parallel to their axes) plays an essential role.

Original language | English (US) |
---|---|

Article number | 021112 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 78 |

Issue number | 2 |

DOIs | |

State | Published - Aug 12 2008 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*78*(2), [021112]. https://doi.org/10.1103/PhysRevE.78.021112

**Vacancy diffusion in the triangular-lattice dimer model.** / Jeng, Monwhea; Bowick, Mark John; Krauth, Werner; Schwarz, Jennifer M; Xing, Xiangjun.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 78, no. 2, 021112. https://doi.org/10.1103/PhysRevE.78.021112

}

TY - JOUR

T1 - Vacancy diffusion in the triangular-lattice dimer model

AU - Jeng, Monwhea

AU - Bowick, Mark John

AU - Krauth, Werner

AU - Schwarz, Jennifer M

AU - Xing, Xiangjun

PY - 2008/8/12

Y1 - 2008/8/12

N2 - We study vacancy diffusion on the classical triangular-lattice dimer model, subject to the kinetic constraint that dimers can only translate, but not rotate. A single vacancy, i.e., a monomer, in an otherwise fully packed lattice, is always localized in a treelike structure. The distribution of tree sizes is asymptotically exponential and has an average of 8.16±0.01 sites. A connected pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of monomers is anomalous: x 2 ∝ tβ, with β=0.46±0.06. We also find that the same exponent β governs diffusion of clusters of three or four monomers, as well as the diffusion of dimers at finite but low monomer densities. We argue that coordinated motion of monomer pairs is the basic mechanism allowing large-scale transport at low monomer densities. We further identify a "swap-tunneling" mechanism for diffusion of monomer pairs, where a subtle interplay between swap moves (translations of dimers transverse to their axes) and glide moves (translations of dimers parallel to their axes) plays an essential role.

AB - We study vacancy diffusion on the classical triangular-lattice dimer model, subject to the kinetic constraint that dimers can only translate, but not rotate. A single vacancy, i.e., a monomer, in an otherwise fully packed lattice, is always localized in a treelike structure. The distribution of tree sizes is asymptotically exponential and has an average of 8.16±0.01 sites. A connected pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of monomers is anomalous: x 2 ∝ tβ, with β=0.46±0.06. We also find that the same exponent β governs diffusion of clusters of three or four monomers, as well as the diffusion of dimers at finite but low monomer densities. We argue that coordinated motion of monomer pairs is the basic mechanism allowing large-scale transport at low monomer densities. We further identify a "swap-tunneling" mechanism for diffusion of monomer pairs, where a subtle interplay between swap moves (translations of dimers transverse to their axes) and glide moves (translations of dimers parallel to their axes) plays an essential role.

UR - http://www.scopus.com/inward/record.url?scp=49549117106&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49549117106&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.78.021112

DO - 10.1103/PhysRevE.78.021112

M3 - Article

AN - SCOPUS:49549117106

VL - 78

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 2

M1 - 021112

ER -