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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2007

Vacancy localization in the square dimer model

Résumé

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 57/4-10$\sqrt{2}$ 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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hal-00336793 , version 1 (25-04-2023)

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Jérémie Bouttier, Mark Bowick, Emmanuel Guitter, Monwhea Jeng. Vacancy localization in the square dimer model. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2007, 76, pp.041140. ⟨10.1103/PhysRevE.76.041140⟩. ⟨hal-00336793⟩
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