Red-green-blue model

Phys. Rev. E 69, 037105 – Published 31 March 2004
David B. Wilson


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 (SLE4) 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

Authors & Affiliations

David B. Wilson

  • Microsoft Research, One Microsoft Way, Redmond, Washington 98052, USA

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