Exact solution of the dimer model: Corner free energy, correlation functions and combinatorics
arXiv:1410.4131 · doi:10.1016/j.nuclphysb.2015.03.022
Abstract
In this work, some classical results of the pfaffian theory of the dimer model based on the work of Kasteleyn, Fisher and Temperley are introduced in a fermionic framework. Then we shall detail the bosonic formulation of the model {\it via} the so-called height mapping and the nature of boundary conditions is unravelled. The complete and detailed fermionic solution of the dimer model on the square lattice with an arbitrary number of monomers is presented, and finite size effect analysis is performed to study surface and corner effects, leading to the extrapolation of the central charge of the model. The solution allows for exact calculations of monomer and dimer correlation functions in the discrete level and the scaling behavior can be inferred in order to find the set of scaling dimensions and compare to the bosonic theory which predict particular features concerning corner behaviors. Finally, some combinatorial and numerical properties of partition functions with boundary monomers are discussed, proved and checked with enumeration algorithms.
Final version to be published in Nuclear Physics B (53 pages and a lot of figures)
References in corpus (22)
- Quantum criticality
- Dimer models and toric diagrams
- Interacting classical dimers on the square lattice
- Classical dimers with aligning interactions on the square lattice
- Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
- Random trimer tilings
- Grassmann Integral Representation for Spanning Hyperforests
- The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary
- Exact solution of close-packed dimers on the kagome lattice
- Rectangular amplitudes, conformal blocks, and applications to loop models
- Corner contribution to percolation cluster numbers
- Dimers on the Triangular Kagome Lattice
- Boundary monomers in the dimer model
- Vacancy localization in the square dimer model
- Close-packed dimers on the kagome lattice: Finite lattices and the Grassmannian approach
- Alternative description of the 2D Blume-Capel model using Grassmann algebra
- Exact entropy of dimer coverings for a class of lattices in three or more dimensions
- Exact Solution of a Monomer-Dimer Problem: A Single Boundary Monomer on a Non-Bipartite Lattice
- Vacancy diffusion in the triangular lattice dimer model
- Finite Size Corrections for Dimers
- Classical and quantum dimers on the star lattice
- Fermions and Disorder in Ising and Related Models in Two Dimensions