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

الأصل · EN

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≥ 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.