Criticality of a classical dimer model on the triangular lattice

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Quantum Many-Body Systems

Background:

• Dimer models are crucial for understanding statistical mechanics and phase transitions.
• Investigating lattice geometries like square and triangular lattices reveals diverse physical behaviors.
• Understanding the role of interactions and chemical potentials is key to predicting emergent phases.

Purpose of the Study:

• To investigate a classical interacting dimer model interpolating between square and triangular lattices.
• To explore the phase diagram as a function of interaction strength and chemical potential.
• To determine the compatibility of criticality and nonbipartiteness in dimer models.

Main Methods:

• Transfer matrix calculations were employed to analyze the model.
• The interaction energy was defined based on plaquette configurations.
• Phase transitions were studied by varying interaction strength and lattice anisotropy.

Main Results:

• In the anisotropic triangular case, a liquid dimer phase, a critical phase, and a columnar phase were observed with increasing interaction.
• The critical phase exhibits similarities to the square lattice dimer model.
• In the isotropic triangular case, a first-order phase transition to an ordered phase was indicated, bypassing a critical phase.

Conclusions:

• Criticality and nonbipartiteness are compatible in this interacting dimer model.
• The study highlights the rich phase behavior achievable by tuning lattice geometry and interactions.
• The findings contribute to the understanding of phase transitions in frustrated magnetic systems and lattice models.