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arXiv · 0706.1016

Vacancy localization in the square dimer model

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

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J. Bouttier, M. Bowick, E. Guitter, M. Jeng. 2007-10-31. Vacancy localization in the square dimer model. https://doi.org/10.1103/physreve.76.041140

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