Pfaffian Correlation Functions of Planar Dimer Covers
Mathematical Physics
2017-09-12 v2 Statistical Mechanics
math.MP
Abstract
The Pfaffian structure of the boundary monomer correlation functions in the dimer-covering planar graph models is rederived through a combinatorial / topological argument. These functions are then extended into a larger family of order-disorder correlation functions which are shown to exhibit Pfaffian structure throughout the bulk. Key tools involve combinatorial switching symmetries which are identified through the loop-gas representation of the double dimer model, and topological implications of planarity.
Cite
@article{arxiv.1609.02824,
title = {Pfaffian Correlation Functions of Planar Dimer Covers},
author = {Michael Aizenman and Manuel Laínz Valcázar and Simone Warzel},
journal= {arXiv preprint arXiv:1609.02824},
year = {2017}
}
Comments
Revised figures; corrected misprints