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On an algebraic approach to Cubic Lattice Potts Models

On an algebraic approach to Cubic Lattice Potts Models
On an algebraic approach to Cubic Lattice Potts Models
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.
0305-4470
263
Dasmahapatra, Srinandan
eb5fd76f-4335-4ae9-a88a-20b9e2b3f698
Martin, Paul
72111efd-2fe6-4258-8f1a-a3aec3cb3d0d
Dasmahapatra, Srinandan
eb5fd76f-4335-4ae9-a88a-20b9e2b3f698
Martin, Paul
72111efd-2fe6-4258-8f1a-a3aec3cb3d0d

Dasmahapatra, Srinandan and Martin, Paul (1996) On an algebraic approach to Cubic Lattice Potts Models. Journal of Physics A: Mathematical and General, 29 (2), 263. (doi:10.1088/0305-4470/29/2/006).

Record type: Article

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.

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Published date: 1996
Organisations: Southampton Wireless Group

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Local EPrints ID: 264095
URI: http://eprints.soton.ac.uk/id/eprint/264095
ISSN: 0305-4470
PURE UUID: 769d5e51-252c-4dbb-acee-def6b377d99a

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Date deposited: 29 May 2007
Last modified: 14 Mar 2024 07:42

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Author: Srinandan Dasmahapatra
Author: Paul Martin

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