Criticality of a classical dimer model on the triangular lattice

Abstract

We consider a classical interacting dimer model which interpolates between the square lattice case and the triangular lattice case by tuning a chemical potential in the diagonal bonds. The interaction energy simply corresponds to the number of plaquettes with parallel dimers. Using transfer matrix calculations, we find in the anisotropic triangular case a succession of different physical phases as the interaction strength is increased: a short range disordered liquid dimer phase at low interactions, then a critical phase similar to the one found for the square lattice, and finally a transition to an ordered columnar phase for large interactions. The existence of the critical phase is in contrast with the belief that criticality for dimer models is ascribed to bipartiteness. For the isotropic triangular case, we have indications that the system undergoes a first order phase transition to an ordered phase, without appearance of an intermediate critical phase.

12 pages, 16 figures

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Cited by in corpus (7)

• Topological ${\mathbb{Z}}_2$ Resonating-Valence-Bond Spin Liquid on the Square Lattice
• Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice
• Entanglement Entropy at Generalized Rokhsar-Kivelson Points of Quantum Dimer Models
• Loop condensation in the triangular lattice quantum dimer model
• Exact Solution and Correlations of a Quantum Dimer Model on the Checkerboard Lattice
• Interacting Fermions Picture for Dimer Models
• Derivation of field theory for the classical dimer model using bosonization