On the Red-Green-Blue Model

TL;DR

This paper experimentally investigates the red-green-blue loop model, revealing its relation to SLE_4 and double-dimer loops under flat boundary conditions, and analyzing its nesting properties and conformal invariance.

Contribution

It provides the first detailed study of the red-green-blue model, connecting it to known loop models and exploring its geometric and conformal properties.

Findings

Red-green-blue loops relate closely to SLE_4 and double-dimer loops.

Red-green-blue loops are more tightly nested than double-dimer loops.

The 2D minimum spanning tree is not conformally invariant.

Abstract

We experimentally study the red-green-blue model, which is a sytem 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 SLE_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 2D minimum spanning tree, and find that it is not conformally invariant.