Vacancy localization in the square dimer model
| dc.creator | Bouttier, J. | |
| dc.creator | Bowick, M. | |
| dc.creator | Guitter, E. | |
| dc.creator | Jeng, M. | |
| dc.date | 2007-06-07 | |
| dc.date | 2007-10-31 | |
| dc.date.accessioned | 2026-07-07T08:39:22Z | |
| dc.date.available | 2026-07-07T08:39:22Z | |
| dc.description | 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/0706.1016 | |
| dc.identifier | http://arxiv.org/abs/0706.1016 | |
| dc.identifier | Phys. Rev. E 76, 041140 (2007) | |
| dc.identifier | doi:10.1103/PhysRevE.76.041140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141046 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Vacancy localization in the square dimer model | |
| dc.type | text |