A triangular gap of size two in a sea of dimers on a $60^\circ$ angle

Mihai Ciucu; Ilse Fischer

A triangular gap of size two in a sea of dimers on a $60^\circ$ angle

Mathematical Physics 2014-05-19 v1 Statistical Mechanics Combinatorics math.MP

Authors: Mihai Ciucu , Ilse Fischer

Abstract

We consider a triangular gap of side two in a $60^\circ$ angle on the triangular lattice whose sides are zig-zag lines. We study the interaction of the gap with the corner as the rest of the angle is completely filled with lozenges. We show that the resulting correlation is governed by the product of the distances between the gap and its five images in the sides of the angle. This provides a new aspect of the parallel between the correlation of gaps in dimer packings and electrostatics developed by the first author in previous work.

Keywords

dimer model triangular lattice triangular gap lozenges correlation function electrostatics analogy zig-zag lines

Cite

@article{arxiv.1405.4235,
  title  = {A triangular gap of size two in a sea of dimers on a $60^\circ$ angle},
  author = {Mihai Ciucu and Ilse Fischer},
  journal= {arXiv preprint arXiv:1405.4235},
  year   = {2014}
}

Comments

21 pages. arXiv admin note: substantial text overlap with arXiv:1403.0925

A triangular gap of size two in a sea of dimers on a $60^\circ$ angle

Abstract

Keywords

Cite

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