Letters in Mathematical Physics

, Volume 30, Issue 3, pp 179–185 | Cite as

Algebras in higher-dimensional statistical mechanics - the exceptional partition (mean field) algebras

  • Paul Martin
  • Hubert Saleur


We determine the structure of the partition algebraPn(Q) (a generalized Temperley-Lieb algebra) for specific values ofQ ∈ ℂ, focusing on the quotient which gives rise to the partition function ofn siteQ-state Potts models (in the continuousQ formulation) in arbitrarily high lattice dimensions (the mean field case). The algebra is nonsemisimple iffQ is a nonnegative integer less than 2n-1. We determine the dimension of the key irreducible representation in every specialization.

Mathematics Subject Classifications (1991)

81R05 82B20 


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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Paul Martin
    • 1
  • Hubert Saleur
    • 2
  1. 1.Mathematics DepartmentCity UniversityLondonU.K.
  2. 2.Physics Department and Mathematics DepartmentUniversity of Southern CaliforniaLos AngelesUSA

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