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• W2019472146 abstract "We construct generalizations Pmn(Q) of the partition algebra Pn(Q) (Martin P P 1996 J. Algebra 183 319), facilitating a representation theoretic approach to the n-site transfer matrix spectrum of a high-dimensional Q-state Potts model with magnetic field and source terms (and to corresponding dichromatic polynomials). For each Q ∊ ℂ we describe the irreducible representation theory of the sequence of algebras P*(Q) = {Pn(Q) ⊂ Pn1(Q) ⊂ Pn + 1(Q)| n = 0,1,2,...} approaching the large-n limit. For each positive integer Q we extend the Potts model representation ρn of Pn(Q) to a representation of P1n(Q). We show how these Potts representations embed in the representation theory of the partition algebras. These results together provide a tool with which to examine the nature of physical correlation functions." @default.
• W2019472146 created "2016-06-24" @default.
• W2019472146 creator A5026873009 @default.
• W2019472146 date "2000-05-05" @default.
• W2019472146 modified "2023-09-27" @default.
• W2019472146 title "The partition algebra and the Potts model transfer matrix spectrum in high dimensions" @default.
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• W2019472146 doi "https://doi.org/10.1088/0305-4470/33/19/304" @default.
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