New Two-color Dimer Models with Critical Ground States

TL;DR

This paper introduces two novel two-color dimer models on the square lattice, utilizing height representations and Monte Carlo simulations to reveal their critical behavior and universality classes.

Contribution

The paper defines new two-color dimer models with critical ground states and analyzes their properties using height representations and Monte Carlo methods.

Findings

Both models exhibit critical correlations.

One model has a smooth height component with correlated fluctuations.

The other model has rough heights with anisotropic critical correlations.

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.