### Abstract

Original language | English |
---|---|

Pages (from-to) | 2957-2963 |

Number of pages | 7 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 391 |

Issue number | 10 |

Early online date | 12 Jan 2012 |

DOIs | |

Publication status | Published - 15 May 2012 |

### Fingerprint

### Keywords

- regular tilings
- degree distribution
- power laws
- finite graph
- statistical mechanics functions
- Penrose tiling

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*391*(10), 2957-2963. https://doi.org/10.1016/j.physa.2012.01.013

}

*Physica A: Statistical Mechanics and its Applications*, vol. 391, no. 10, pp. 2957-2963. https://doi.org/10.1016/j.physa.2012.01.013

**Statistical mechanics of two-dimensional tilings.** / Kaatz, F.H.; Estrada, Ernesto; Bultheel, A.; Sharrock, N.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Statistical mechanics of two-dimensional tilings

AU - Kaatz, F.H.

AU - Estrada, Ernesto

AU - Bultheel, A.

AU - Sharrock, N.

PY - 2012/5/15

Y1 - 2012/5/15

N2 - Reduced dimensionality in two dimensions is a topic of current interest. We use model systems to investigate the statistical mechanics of ideal networks. The tilings have possible applications such as the 2D locations of pore sites in nanoporous arrays (quantum dots), in the 2D hexagonal structure of graphene, and as adsorbates on quasicrystalline crystal surfaces. We calculate the statistical mechanics of these networks, such as the partition function, free energy, entropy, and enthalpy. The plots of these functions versus the number of links in the finite networks result in power law regression. We also determine the degree distribution, which is a combination of power law and rational function behavior. In the large-scale limit, the degree of these 2D networks approaches 3, 4, and 6, in agreement with the degree of the regular tilings. In comparison, a Penrose tiling has a degree also equal to about 4.

AB - Reduced dimensionality in two dimensions is a topic of current interest. We use model systems to investigate the statistical mechanics of ideal networks. The tilings have possible applications such as the 2D locations of pore sites in nanoporous arrays (quantum dots), in the 2D hexagonal structure of graphene, and as adsorbates on quasicrystalline crystal surfaces. We calculate the statistical mechanics of these networks, such as the partition function, free energy, entropy, and enthalpy. The plots of these functions versus the number of links in the finite networks result in power law regression. We also determine the degree distribution, which is a combination of power law and rational function behavior. In the large-scale limit, the degree of these 2D networks approaches 3, 4, and 6, in agreement with the degree of the regular tilings. In comparison, a Penrose tiling has a degree also equal to about 4.

KW - regular tilings

KW - degree distribution

KW - power laws

KW - finite graph

KW - statistical mechanics functions

KW - Penrose tiling

UR - http://www.scopus.com/inward/record.url?scp=84857625858&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2012.01.013

DO - 10.1016/j.physa.2012.01.013

M3 - Article

VL - 391

SP - 2957

EP - 2963

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 10

ER -