Jamming probabilities for a vacancy in the dimer model

TL;DR

This paper analytically investigates the mobility and jamming probabilities of a single vacancy in the close-packed dimer model on a square lattice, providing exact calculations for these properties.

Contribution

It introduces a determinantal approach using spanning web representation to compute vacancy mobility and jamming probabilities in the dimer model.

Findings

Exact probability for vacancy to be jammed

Determinantal expressions for mobility properties

Reduction to Toeplitz determinants for large lattices

Abstract

Following the recent proposal made by Bouttier et al [Phys. Rev. E 76, 041140 (2007)], we study analytically the mobility properties of a single vacancy in the close-packed dimer model on the square lattice. Using the spanning web representation, we find determinantal expressions for various observable quantities. In the limiting case of large lattices, they can be reduced to the calculation of Toeplitz determinants and minors thereof. The probability for the vacancy to be strictly jammed and other diffusion characteristics are computed exactly.