Publication : t07/070
Vacancy localization in the square dimer model
Bouttier J. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)Bowick M.J. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Guitter E. (CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE)
Jeng M. (Physics Department, Syracuse University, 201 Physics Building, Syracuse, NY 13244-1130, USA)
Abstract:Année de publication : 2007
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.
Revue : Phys. Rev. E 76 041140 (2007)
DOI : 10.1103/PhysRevE.76.041140
Preprint : arXiv:0706.1016
PACS : 05.50.+q, 02.10.Ox, 68.55.Ln
Langue : Anglais
Fichier(s) à télécharger :
0706.1016v2 PhysRevE.76.041140.pdf eprint_publi.tar.gz ps_publi.ps
