Algebras in Higher Dimensional Statistical Mechanics - the Exceptional Partition (MEAN Field) Algebras

Details Algebras in Higher Dimensional Statistical Mechanics - the Exceptional Partition (MEAN Field) Algebras Algebras in Higher Dimensional Statistical Mechanics - the Exceptional Partition (MEAN Field) Algebras

1993-02-19

arxiv.org/abs/hep-th/9302095v1

Physics

High Energy Physics

High Energy Physics - Theory

4 pages

Scientific paper

10.1007/BF00805850

We determine the structure of the partition algebra $P_n(Q)$ (a generalized Temperley-Lieb algebra) for specific values of $Q \in \C$, focusing on the quotient which gives rise to the partition function of $n$ site $Q$-state Potts models (in the continuous $Q$ formulation) in arbitrarily high lattice dimensions (the mean field case). The algebra is non-semi-simple iff $Q$ is a non-negative integer less than $n$. We determine the dimension of the key irreducible representation in every specialization.

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