TY - JOUR

T1 - Vacancy localization in the square dimer model

AU - Bouttier, J.

AU - Bowick, M.

AU - Guitter, E.

AU - Jeng, M.

PY - 2007/10/30

Y1 - 2007/10/30

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevE.76.041140

DO - 10.1103/PhysRevE.76.041140

M3 - Article

AN - SCOPUS:35648930924

SN - 1063-651X

VL - 76

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 4

M1 - 041140

ER -