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.
Highlights
Symmetry-breaking phase transitions can be described using an ‘order parameter,’ a local observable that transforms nontrivially under the symmetries, and which is strictly zero in the disordered phase but nonzero in the ordered phase [1]
As for the same model on the cubic lattice [15], we find a transition without any symmetry breaking, between a standard ‘Coulomb’ phase [12] and a ‘synchronized’ phase, where both replicas remain disordered but their relative fluctuations are suppressed
We have previously identified such a phase, which we call ‘synchronized’, in the double dimer model on the cubic lattice [15], and we demonstrate in the following that it occurs on the square lattice
Summary
Symmetry-breaking phase transitions can be described using an ‘order parameter,’ a local observable that transforms nontrivially under the symmetries, and which is strictly zero in the disordered phase but nonzero in the ordered phase [1]. The configuration space splits into ‘topological sectors’ corresponding to distinct values of the flux through each spanning surface, with a global rearrangement of dimers required to change sector This allows for the possibility of phases distinguished by the flux variance, which can be either suppressed exponentially or nonzero in the thermodynamic limit. Of either sign, both between parallel dimers within each replica, , as studied previously in the single dimer model [13, 14], and between dimers that coincide (or ‘overlap’) in the two replicas, We show that it exhibits a rich phase structure, including a number of phases with distinct types of order, both topological and symmetry-breaking.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
