Boundary monomers in the dimer model

Abstract

The correlation functions of an arbitrary number of boundary monomers in the system of close-packed dimers on the square lattice are computed exactly in the scaling limit. The equivalence of the 2n-point correlation functions with those of a complex free fermion is proved, thereby reinforcing the description of the monomer-dimer model by a conformal free field theory with central charge c=1.

15 pages, 2 figures

References in corpus (9)

• Classical dimers on the triangular lattice
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Logarithmic Conformal Field Theory and Boundary Effects in the Dimer Model
• Pocket Monte Carlo algorithm for classical doped dimer models
• Pre-logarithmic and logarithmic fields in a sandpile model
• Monomer-dimer model in two-dimensional rectangular lattices with fixed dimer density
• Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries
• The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary
• Wind on the boundary for the Abelian sandpile model

Cited by in corpus (12)

• Return probability for the loop-erased random walk and mean height in sandpile : a proof
• Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatorics
• Integrability and conformal data of the dimer model
• Dimers and analytic torsion I
• Non-Local Finite-Size Effects in the Dimer Model
• Refined conformal spectra in the dimer model
• A Pfaffian formula for monomer-dimer partition functions
• Grassmannian representation of the two-dimensional monomer-dimer model
• Pfaffian Correlation Functions of Planar Dimer Covers
• A Statistical Model of Current Loops and Magnetic Monopoles
• Entropy and chirality in sphinx tilings
• A Pfaffian formula for the monomer-dimer model on surface graphs