Non-Local Finite-Size Effects in the Dimer Model

Abstract

We study the finite-size corrections of the dimer model on $\infty \times N$ square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections depend in a crucial way on the parity of $N$, and show that, because of certain non-local features present in the model, a change of parity of $N$ induces a change of boundary condition. Taking a careful account of this, these unusual finite-size behaviours can be fully explained in the framework of the $c=-2$ logarithmic conformal field theory.

This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (13)

• Classical dimers on the triangular lattice
• Logarithmic Conformal Field Theory and Boundary Effects in the Dimer Model
• Height variables in the Abelian sandpile model: scaling fields and correlations
• A c=-2 boundary changing operator for the Abelian sandpile
• Kronecker's Double Series and Exact Asymptotic Expansion for Free Models of Statistical Mechanics on Torus
• Dimer statistics on the Möbius strip and the Klein bottle
• Logarithmic scaling for height variables in the Abelian sandpile model
• Random trimer tilings
• Close-packed dimers on nonorientable surfaces
• The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary
• Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries
• Boundary monomers in the dimer model
• Dimers on a simple-quartic net with a vacancy

Cited by in corpus (7)

• Vacancy localization in the square dimer model
• Yang-Baxter Solution of Dimers as a Free-Fermion Six-Vertex Model
• Sandpile models in the large
• Exact finite-size corrections in the dimer model on a planar square lattice
• Yang-Baxter Integrable Dimers on a Strip
• Finite-size scaling of free energy in the dimer model on a hexagonal domain
• Exact finite-size corrections in the dimer model on a cylinder