On the algebraic approach to cubic lattice Potts models

Details On the algebraic approach to cubic lattice Potts models On the algebraic approach to cubic lattice Potts models

1995-12-13

arxiv.org/abs/hep-th/9512093v1

J.Phys.A29:263-278,1996

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, in LaTeX (to be published in J. Phys. A)

Scientific paper

10.1088/0305-4470/29/2/006

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.

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