Interacting double dimer model on the square lattice

Wilkins, Neil; Powell, Stephen

Abstract

We study phases and transitions of the square-lattice double dimer model, consisting of two coupled replicas of the classical dimer model. As on the cubic lattice, we find a thermal phase transition from the Coulomb phase, a disordered but correlated dimer liquid, to a phase where fluctuations of the two replicas are closely synchronized with one another. Surprisingly, and in contrast to the cubic case, the phase boundary includes the noninteracting point, as we establish using a symmetry-based analysis of an effective height theory, indicating that infinitesimal coupling is sufficient to synchronize the double dimer model. In addition, we observe a novel antisynchronized phase when the coupling between replicas is repulsive, and use Monte Carlo simulations to establish the full phase diagram, including (anti)synchronized columnar and staggered phases, with interactions between parallel dimers in each replica.

Citation

Wilkins, N., & Powell, S. (2020). Interacting double dimer model on the square lattice. Physical Review B, 102(17), Article 174431. https://doi.org/10.1103/PhysRevB.102.174431

• Journal Article Type: Article
• Acceptance Date: Oct 30, 2020
• Online Publication Date: Nov 19, 2020
• Publication Date: Nov 19, 2020
• Deposit Date: Nov 16, 2020
• Publicly Available Date: Nov 19, 2020
• Journal: Physical Review B
• Print ISSN: 2469-9950
• Electronic ISSN: 2469-9969
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 102
• Issue: 17
• Article Number: 174431
• DOI: https://doi.org/10.1103/PhysRevB.102.174431
• Public URL: https://nottingham-repository.worktribe.com/output/5047200
• Publisher URL: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.102.174431