On the algebraic approach to cubic lattice Potts models
Abstract
We consider Diagram algebras, $\Dg(G)$ (generalized Temperley-Lieb algebras) defined for a large class of graphs
G
, including those of relevance for cubic lattice Potts models, and study their structure for generic
Q
. We find that these algebras are too large to play the precisely analogous role in three dimensions to that played by the Temperley-Lieb algebras for generic
Q
in the planar case. We outline measures to extract the quotient algebra that would illuminate the physics of three dimensional Potts models.