#### Document Type

Article

#### Date

10-31-2007

#### Language

English

#### Disciplines

Physics

#### Description/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 57/4-10Sqrt[2] 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 9/8. 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 1/4. 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.

#### Repository Citation

Bowick, Mark; Bouttier, J.; Guitter, Emmanuel; and Jeng, Monwhea, "Vacancy Localization in the Square Dimer Model" (2007). *Physics.* Paper 146.

http://surface.syr.edu/phy/146

#### Source

Harvested from Arxiv.org

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 3.0 License.

## Additional Information

35 pages, 24 figures. Improved version with one added figure (figure 9), a shift s->s+1 in the definition of the tree size, and minor corrections More information at http://arxiv.org/abs/0706.1016