New two-color dimer models with critical ground states |
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Authors: | R Raghavan Christopher L Henley Scott L Arouh |
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Institution: | (1) Laboratory of Atomic and Solid State Physics, 14853-2501 Ithaca, New York;(2) Present address: 70 Remsen St., Apt. 7G, 11201 Brooklyn, New York;(3) Present address: Department of Physics, University of California-San Diego, 92093 La Jolla, California |
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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. |
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Keywords: | Dimer packing fully packed loop model height model classical spin models solid-on-solid models Coulomb gas Monte Carlo simulations |
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