Synchronization transition in the double dimer model on the cubic lattice

Wilkins, Neil; Powell, Stephen

Abstract

We study the classical cubic-lattice double dimer model, consisting of two coupled replicas of the close-packed dimer model, using a combination of theoretical arguments and Monte Carlo simulations. Our results establish the presence of a 'synchronization transition' at a critical value of the coupling, where both replicas remain disordered but their fluctuations become strongly correlated. We show that this unconventional transition, which has neither external nor spontaneous symmetry breaking, is continuous and belongs to the 3D inverted-XY universality class. By adding aligning interactions for dimers within each replica, we map out the full phase diagram including the interplay between columnar ordering and synchronization. We also solve the coupled double dimer model exactly on the Bethe lattice and show that it correctly reproduces the qualitative phase structure, but with mean-field critical behavior.

Citation

Wilkins, N., & Powell, S. (2019). Synchronization transition in the double dimer model on the cubic lattice. Physical Review B, 99(14), Article 144403. https://doi.org/10.1103/PhysRevB.99.144403

• Journal Article Type: Article
• Acceptance Date: Mar 15, 2019
• Online Publication Date: Apr 1, 2019
• Publication Date: Apr 1, 2019
• Deposit Date: Mar 21, 2019
• Publicly Available Date: Mar 28, 2019
• Journal: Physical Review B
• Print ISSN: 2469-9950
• Electronic ISSN: 2469-9969
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 99
• Issue: 14
• Article Number: 144403
• DOI: https://doi.org/10.1103/PhysRevB.99.144403
• Public URL: https://nottingham-repository.worktribe.com/output/1674452
• Publisher URL: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.99.144403
• Additional Information: ©2019 American Physical Society
• Contract Date: Mar 28, 2019