Dimer-dimer correlations at the rough-smooth boundary
Abstract
Three phases of macroscopic domains have been seen for large but finite periodic dimer models; these are known as the frozen, rough and smooth phases. The transition region between the frozen and rough region has received a lot of attention for the last twenty years and recently work has been underway to understand the rough-smooth transition region in the case of the two-periodic Aztec diamond. We compute uniform asymptotics for dimer-dimer correlations of the two-periodic Aztec diamond when the dimers lie in the rough-smooth transition region. These asymptotics rely on a formula found in [5] for the inverse Kasteleyn matrix, they also apply to a related infinite dimer model.
Cite
@article{arxiv.2110.14505,
title = {Dimer-dimer correlations at the rough-smooth boundary},
author = {Kurt Johansson and Scott Mason},
journal= {arXiv preprint arXiv:2110.14505},
year = {2022}
}
Comments
The introduction was expanded, the numbering of corollaries in section 3 was altered, a minor mistake was fixed in equation (74) and a simplification was made (see remark 1)