Vacancy diffusion in the triangular lattice dimer model

TL;DR

This study investigates how vacancies (monomers) move in a triangular lattice dimer model with translation-only dynamics, revealing localization for single vacancies and anomalous diffusion for pairs, with implications for understanding constrained lattice systems.

Contribution

It provides the first detailed analysis of vacancy diffusion under kinetic constraints in the triangular lattice dimer model, highlighting localization and delocalization phenomena.

Findings

Single vacancies are localized in tree-like structures with exponential size distribution.

Pairs of vacancies can delocalize and diffuse anomalously.

Average tree size for localization is approximately 8 sites.

Abstract

We study vacancy diffusion on the classical triangular lattice dimer model, sub ject 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 \pm 0.01 sites. A connected pair of monomers has a finite probability of being delocalized. When delocalized, the diffusion of monomers is anomalous: