Monomer-Dimer Mixture on a Honeycomb Lattice

Abstract

We study a monomer-dimer mixture defined on a honeycomb lattice as a toy model for the spin ice system in a magnetic field. In a low-doping region of monomers, the effective description of this system is given by the dual sine-Gordon model. In intermediate- and strong-doping regions, the Potts lattice gas theory can be employed. Synthesizing these results, we construct a renormalization-group flow diagram, which includes the stable and unstable fixed points corresponding to ${\mathcal{M}}_5$ and ${\mathcal{M}}_6$ in the minimal models of the conformal field theory. We perform numerical transfer-matrix calculations to determine a global phase diagram and also to proffer evidence to check our prediction.

5 pages, 3 figures

References in corpus (17)

• Magnetic Monopoles in Spin Ice
• Dirac Strings and Magnetic Monopoles in Spin Ice Dy2Ti2O7
• Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets
• Ising models of quantum frustration
• Magnetic Charge Transport
• Why spin ice obeys the ice rules
• A new macroscopically degenerate ground state in the spin ice compound Dy2Ti2O7 under a magnetic field
• Observation of Magnetic Monopoles in Spin Ice
• Relaxation time for a dimer covering with height representation
• Specific Heat of Kagome Ice in the Pyrochlore Oxide Dy2Ti2O7
• Interacting classical dimers on the square lattice
• Criticality in self-dual sine-Gordon models
• Magnetization process of spin ice in a [111] magnetic field
• Kagomé ice state in the dipolar spin ice Dy_{2}Ti_{2}O_{7}
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• The semiflexible fully-packed loop model and interacting rhombus tilings
• Classical dimer model with anisotropic interactions on the square lattice

Cited by in corpus (5)

• Magnetic charge and ordering in kagome spin ice
• Stiffness from Disorder in Triangular-Lattice Ising Thin Films
• Ordering phenomena in a heterostructure of frustrated and unfrustrated triangular-lattice Ising layers
• Exact Results for the Residual Entropy of Ice Hexagonal Monolayer
• Universal Renyi mutual information in classical systems: the case of kagome ice