Derivation of field theory for the classical dimer model using bosonization

TL;DR

This paper develops a field theory for the 2D classical dimer model using bosonization, confirming known height theory results, fixing coefficients, and analyzing phase boundaries with interactions.

Contribution

It provides a constructive derivation of the field theory from microscopic transfer-matrix solutions, including interaction effects and phase boundary analysis.

Findings

Results consistent with height theory

Coefficients in the effective theory are explicitly fixed

Phase boundary shape near noninteracting point determined

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.