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Synchronization transition in the double dimer model on the cubic lattice

Wilkins, Neil; Powell, Stephen

Synchronization transition in the double dimer model on the cubic lattice Thumbnail


Neil Wilkins


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.

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
Public URL
Publisher URL
Additional Information ©2019 American Physical Society


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