Interacting double dimer model on the square lattice

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.

arXiv comment17 pages, 11 figures, 1 table; v2: improved discussion of critical properties in section IV C plus other minor changes

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Cited by in corpus (10)

• Fully packed quantum loop model on the square lattice: phase diagram and application for Rydberg atoms
• Emergent Fracton Dynamics in a Non-Planar Dimer Model
• Bilayer Coulomb phase of two dimensional dimer models: Absence of power-law columnar order
• Re-entrance effect in the high-temperature critical phase of the quantum dimer model on the square lattice
• Asymptotic Freedom at the Berezinskii-Kosterlitz-Thouless Transition without Fine-Tuning Using a Qubit Regularization
• Ashkin-Teller phase transition and multicritical behavior in a classical monomer-dimer model
• Quantum Kasteleyn transition
• Classical fully-packed loop model with attractive interactions on the square lattice
• Derivation of field theory for the classical dimer model using bosonization
• Dynamic scaling theory for a field quench near the Kasteleyn transition in spin ice