New Two-color Dimer Models with Critical Ground States

Abstract

We define two new models on the square lattice, in which each allowed configuration is a superposition of a covering by ``white'' dimers and one by ``black'' dimers. Each model maps to a solid-on-solid (SOS) model in which the ``height'' field is two dimensional. Measuring the stiffness of the SOS fluctuations in the rough phase provides critical exponents of the dimer models. Using this ``height'' representation, we have performed Monte Carlo simulations. They confirm that each dimer model has critical correlations and belongs to a new universality class. In the "dimer-loop" model (which maps to a loop model) one height component is smooth but has unusual correlated fluctuations; the other height component is rough. In the ``noncrossing-dimer'' model, the heights are rough having two different elastic constants; an unusual form of its elastic theory implies anisotropic critical correlations.

19 pages, plain TeX; 8 figures and 1 table in 20 PostScript files. Replacement to add journal ref

References in corpus (2)

• Kac-Moody Symmetries of Critical Ground States
• Exact Results for Hamiltonian Walks from the Solution of the Fully Packed Loop Model on the Honeycomb Lattice

Cited by in corpus (28)

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• Power-law spin correlations in pyrochlore antiferromagnets
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• Relaxation time for a dimer covering with height representation
• Interacting classical dimers on the square lattice
• Monte Carlo simulation of ice models
• Classical dimers with aligning interactions on the square lattice
• Field theory of compact polymers on the square lattice
• Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models
• Liouville Field Theory of Fluctuating Loops
• The 3-State Square-Lattice Potts Antiferromagnet at Zero Temperature
• A constrained Potts antiferromagnet model with an interface representation
• Columnar order and Ashkin-Teller criticality in mixtures of hard-squares and dimers
• Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice
• Exotic quantum liquids in Bose-Hubbard models with spatially-modulated symmetries
• Statistical mechanics of dimers on quasiperiodic Ammann-Beenker tilings
• Resonating valence-bond physics on the honeycomb lattice
• The three-state Potts antiferromagnet on plane quadrangulations
• Interacting double dimer model on the square lattice
• The packing of two species of polygons on the square lattice
• Criticality of a classical dimer model on the triangular lattice
• Fermionic quantum dimer and fully-packed loop models on the square lattice
• Synchronization transition in the double dimer model on the cubic lattice
• Bicolor loop models and their long range entanglement
• Geometric properties of loop condensed phases on the square lattice
• Gauge-Free Duality in Pure Square Spin Ice: Topological Currents and Monopoles
• Quantum lozenge tiling and entanglement phase transition
• Derivation of field theory for the classical dimer model using bosonization