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Jamming probabilities for a vacancy in the dimer model.

V S Poghosyan¹, V B Priezzhev, P Ruelle

¹Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 4, 2008

Summary

This summary is machine-generated.

We analytically study vacancy mobility in the close-packed dimer model on a square lattice. Exact calculations reveal diffusion characteristics and jamming probabilities using determinantal expressions.

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Area of Science:

Statistical Mechanics
Condensed Matter Physics
Mathematical Physics

Background:

The behavior of vacancies in lattice models is crucial for understanding material properties.
The close-packed dimer model on a square lattice provides a simplified yet relevant system for studying diffusion.

Purpose of the Study:

To analytically investigate the mobility properties of a single vacancy.
To extend the understanding of vacancy dynamics based on a recent theoretical proposal.

Main Methods:

Utilizing the spanning web representation for analytical calculations.
Deriving determinantal expressions for observable quantities.
Reducing calculations to Toeplitz determinants and minors for large lattices.

Main Results:

Obtained exact expressions for various observable quantities related to vacancy mobility.
Computed the probability of a vacancy being strictly jammed.
Characterized other diffusion properties of the vacancy.

Conclusions:

The study provides exact analytical results for vacancy diffusion in the specified model.
The methods employed offer a powerful framework for analyzing similar lattice models.
The findings contribute to the fundamental understanding of vacancy-mediated transport phenomena.