Classical Dimer Model on the Square Bilayer Lattice

We study the Classical Dimer Model (CDM) on the square bilayer lattice with the fugacity of interlayer dimers as a tuning parameter. The square monolayer CDM is one of the paradigmatic model of a “Couloumb” phases whose distinct signatures are a) power law correlations in real space, and b) “pinch points” in the “transverse” form of structure factors in momentum space. Here we find that for low fugacity, the square bilayer CDM again hosts Coulomb phases with power law correlations. The pinch point phenomenology is however crucially different than the monolayer. This is integrally related to presence of longitudinal modes and Couloumb correlations together in the bilayer CDM ensemble. For high fugacity, it hosts a featureless phase with predominantly interlayer dimers and exponentially decaying correlations. Remarkably, even though the two phases are not symmetry related, numerical evidence from system sizes upto 512 × 512 points to a continuous transition rather than first-order. We provide an effective “electrostatic” description of the numerical data for low fugacities with the interlayer dimers interpreted as spontaneously fluctuating charged dipole defects.