Derivation of field theory for the classical dimer model using bosonization

Wilkins, Neil; Powell, Stephen

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.

Citation

Wilkins, N., & Powell, S. (2023). Derivation of field theory for the classical dimer model using bosonization. Physical Review E, 107(5), Article 054126. https://doi.org/10.1103/PhysRevE.107.054126

• Journal Article Type: Article
• Acceptance Date: May 1, 2023
• Online Publication Date: May 22, 2023
• Publication Date: May 1, 2023
• Deposit Date: May 3, 2023
• Publicly Available Date: May 3, 2023
• Journal: Physical Review E
• Print ISSN: 2470-0045
• Electronic ISSN: 2470-0053
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 107
• Issue: 5
• Article Number: 054126
• DOI: https://doi.org/10.1103/PhysRevE.107.054126
• Keywords: Effective field theory; Frustrated magnetism; Lattice models in statistical physics; Bosonization; Second quantization; Transfer matrix calculations
• Public URL: https://nottingham-repository.worktribe.com/output/20280567
• Publisher URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.054126