We experimentally study the red-green-blue model, which is a system of loops obtained by superimposing three dimer coverings on offset hexagonal lattices. We find that when the boundary conditions are “flat,” the red-green-blue loops are closely related to stochastic Loewner evolution with parameter κ=4 and double-dimer loops, which are the loops formed by superimposing two dimer coverings of the Cartesian lattice. But we also find that the red-green-blue loops are more tightly nested than the double-dimer loops. We also investigate the two-dimensional minimum spanning tree, and find that it is not conformally invariant.
- Received 3 December 2002
- Published 31 March 2004
© 2004 The American Physical Society