# Jeng Bowick Krauth Schwarz Xing 2008

### From Werner KRAUTH

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**M. Jeng, M. J. Bowick, W. Krauth, J. Schwarz, X. Xing** * Vacancy diffusion in the triangular lattice dimer model* Physical Review E 78 021112 (2008)

**Abstract:**
We study vacancy diffusion on the classical triangular lattice dimer model, subject to the kinetic
constraint that dimers can only translate, but not rotate. A single vacancy, i.e. a monomer,
in an otherwise fully packed lattice, is always localized in a tree-like structure. The distribution
of tree sizes is asymptotically exponential and has an average of 8.16 ± 0.01 sites. A connected
pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of
monomers is anomalous: x² ∝ t^beta�, with beta = 0.46 ± 0.06. We also find that the same exponent
β governs diffusion of clusters of three or four monomers, as well as the diffusion of dimers at
finite but low monomer densities. We argue that coordinated motion of monomer pairs is the basic
mechanism allowing large-scale transport at low monomer densities. We further identify a “swaptunneling”
mechanism for diffusion of monomer pairs, where a subtle interplay between swap moves
(translations of dimers transverse to their axes) and glide moves (translations of dimers parallel to
their axes) plays an essential role.