New Two-color Dimer Models with Critical Ground States

Details New Two-color Dimer Models with Critical Ground States New Two-color Dimer Models with Critical Ground States

1996-06-29

arxiv.org/abs/cond-mat/9606220v2

J. Stat. Phys. 86, 517 (1997)

Physics

Condensed Matter

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

Scientific paper

10.1007/BF02199112

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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