Vacancy localization in the square dimer model

J. Bouttier, M. Bowick, E. Guitter, M. Jeng

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11 Scopus citations


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 languageEnglish (US)
Article number041140
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number4
StatePublished - Oct 30 2007

ASJC Scopus subject areas

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


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