Derivation of field theory for the classical dimer model using bosonization

Abstract

We derive a field theory for the two-dimensional classical dimer model by applying bosonization to Lieb's (fermionic) transfer-matrix solution. Our constructive approach gives results that are consistent with the well-known height theory, previously justified based on symmetry considerations, but also fixes coefficients appearing in the effective theory and the relationship between microscopic observables and operators in the field theory. In addition, we show how interactions can be included in the field theory perturbatively, treating the case of the double dimer model with interactions within and between the two replicas. Using a renormalization-group analysis, we determine the shape of the phase boundary near the noninteracting point, in agreement with results of Monte Carlo simulations.

20 pages, 4 figures, 1 table

References in corpus (11)

• Interacting classical dimers on the square lattice
• Classical dimers with aligning interactions on the square lattice
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Coulomb gas transitions in three-dimensional classical dimer models
• Fermionic Quasiparticle Representation of Tomonaga-Luttinger Hamiltonian
• Unconventional continuous phase transition in a three dimensional dimer model
• Class of exactly soluble models of one-dimensional spinless fermions and its application to the Tomonaga-Luttinger Hamiltonian with nonlinear dispersion
• Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatorics
• Criticality of a classical dimer model on the triangular lattice
• Height fluctuations in non-integrable classical dimers