New sum rule identities and duality relation for the Potts $n$-point correlation function

Details New sum rule identities and duality relation for the Potts $n$-point correlation function New sum rule identities and duality relation for the Potts $n$-point correlation function

1997-06-25

arxiv.org/abs/cond-mat/9706252v1

Physical Review Letters 79, 4954-4957 (1997).

Physics

Condensed Matter

Statistical Mechanics

11 pages in RevTeX, 4 PS figures, submitted to PRL

Scientific paper

10.1103/PhysRevLett.79.4954

It is shown that certain sum rule identities exist which relate correlation functions for $n$ Potts spins on the boundary of a planar lattice for $n\geq 4$. Explicit expressions of the identities are obtained for $n=4,5$. It is also shown that the identities provide the missing link needed for a complete determination of the duality relation for the $n$-point correlation function. The $n=4$ duality relation is obtained explicitly. More generally we deduce the number of correlation identities for any $n$ as well as an inversion relation and a conjecture on the general form of the duality relation.

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