Algebras in Higher Dimensional Statistical Mechanics - the Exceptional Partition (MEAN Field) Algebras
Abstract
We determine the structure of the partition algebra Pn(Q) (a generalized Temperley-Lieb algebra) for specific values of Q ∈ , 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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