Classical dimer model with anisotropic interactions on the square lattice

Abstract

We discuss phase transitions and the phase diagram of a classical dimer model with anisotropic interactions defined on a square lattice. For the attractive region, the perturbation of the orientational order parameter introduced by the anisotropy causes the Berezinskii-Kosterlitz-Thouless transitions from a dimer-liquid to columnar phases. According to the discussion by Nomura and Okamoto for a quantum-spin chain system [J. Phys. A 27, 5773 (1994)], we proffer criteria to determine transition points and also universal level-splitting conditions. Subsequently, we perform numerical diagonalization calculations of the nonsymmetric real transfer matrices up to linear dimension specified by L=20 and determine the global phase diagram. For the repulsive region, we find the boundary between the dimer-liquid and the strong repulsion phases. Based on the dispersion relation of the one-string motion, which exhibits a two-fold ``zero-energy flat band'' in the strong repulsion limit, we give an intuitive account for the property of the strong repulsion phase.

11 pages, 8 figures

References in corpus (21)

• An RVB phase in the triangular lattice quantum dimer model
• Topological Order and Conformal Quantum Critical Points
• Relaxation time for a dimer covering with height representation
• Classical dimers on the triangular lattice
• Interacting classical dimers on the square lattice
• Classical dimers with aligning interactions on the square lattice
• Correlation functions of the 2D sine-Gordon model
• Kac-Moody Symmetries of Critical Ground States
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Generic mixed columnar-plaquette phases in Rokhsar-Kivelson models
• Exact ground states of a frustrated 2D magnet: deconfined fractional excitations at a first order quantum phase transition
• Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system
• The semiflexible fully-packed loop model and interacting rhombus tilings
• Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder
• Field-induced Berezinskii-Kosterlitz-Thouless transition and string-density plateau in the anisotropic triangular antiferromagnetic Ising model
• Level spectroscopy of the square-lattice three-state Potts model with a ferromagnetic next-nearest-neighbor coupling
• Phase separation as an instability of the Tomonaga-Luttinger liquid
• Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: Level-spectroscopy approach
• Critical intermediate phase and phase transitions in a triangular-lattice three-spin interaction model: Level-spectroscopy approach
• Relation between directed polymers in random media and random bond dimer models

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• Monomer-Dimer Mixture on a Honeycomb Lattice
• Interacting Fermions Picture for Dimer Models
• CTMRG study of the critical behavior of an interacting-dimer model