Pfaffian Correlation Functions of Planar Dimer Covers

TL;DR

This paper rederives the Pfaffian structure of boundary monomer correlations in planar dimer models and extends it to bulk order-disorder correlations using combinatorial and topological methods.

Contribution

It provides a new combinatorial and topological derivation of Pfaffian correlation functions and extends these results to a broader class of bulk correlations.

Findings

Pfaffian structure of boundary monomer correlations rederived

Extension of Pfaffian structure to bulk order-disorder correlations

Identification of combinatorial symmetries via loop-gas representation

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.