Pfaffian Correlation Functions of Planar Dimer Covers
arXiv:1609.02824 · doi:10.1007/s10955-016-1684-8
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.
arXiv commentRevised figures; corrected misprints
References in corpus (6)
- Local statistics for random domino tilings of the Aztec diamond
- Exact solution of the dimer model: Corner free energy, correlation functions and combinatorics
- Boundary monomers in the dimer model
- Grassmannian representation of the two-dimensional monomer-dimer model
- A Pfaffian formula for monomer-dimer partition functions
- A Statistical Model of Current Loops and Magnetic Monopoles