Vacancy localization in the square dimer model

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. The motion of a vacancy induced by dimer slidings is analyzed including the size distribution of the domain accessible to the vacancy and the probability for a 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. In 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 $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 4$} $. The resultant weak localization of vacancies still allows for unbounded diffusion with a diffusion exponent related to that of diffusion on spanning trees.