The Pfaffian Sign Theorem for the Dimer Model on a Triangular Lattice
Mathematical Physics
2018-04-18 v2 math.MP
Abstract
We prove the Pfaffian Sign Theorem for the dimer model on a triangular lattice embedded in the torus. More specifically, we prove that the Pfaffian of the Kasteleyn periodic-periodic matrix is negative, while the Pfaffians of the Kasteleyn periodic-antiperiodic, antiperiodic-periodic, and antiperiodic-antiperiodic matrices are all positive. The proof is based on the Kasteleyn identities and on small weight expansions. As an application, we obtain an asymptotics of the dimer model partition function with an exponentially small error term.
Cite
@article{arxiv.1711.00032,
title = {The Pfaffian Sign Theorem for the Dimer Model on a Triangular Lattice},
author = {Pavel Bleher and Brad Elwood and Dražen Petrović},
journal= {arXiv preprint arXiv:1711.00032},
year = {2018}
}
Comments
32 pages, 10 figures