### Abstract

We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this formalism, we can address the question of the possible motion of the vacancy induced by dimer slidings. We find a probability 574-102 for the vacancy to be strictly jammed in an infinite system. More generally, the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 98. On a finite system, the probability that a vacancy in the bulk can reach the boundary falls off as a power law of the system size with exponent 14. The resultant weak localization of vacancies still allows for unbounded diffusion, characterized by a diffusion exponent that we relate to that of diffusion on spanning trees. We also implement numerical simulations of the model with both free and periodic boundary conditions.

Original language | English (US) |
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Article number | 041140 |

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

Volume | 76 |

Issue number | 4 |

DOIs | |

State | Published - Oct 30 2007 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

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

*76*(4), [041140]. https://doi.org/10.1103/PhysRevE.76.041140