Sum Rule Identities and the Duality Relation for the Pottsn-Point Boundary Correlation Function

1997/06/25 by F. Y. Wu, H. Y. Huang
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.79.4954

published as Physical Review Letters 79, 4954-4957 (1997). · 11 pages in RevTeX, 4 PS figures, submitted to PRL

arxiv created 1997/06/25 · openalex publication_date 1997/12/22 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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\ensuremath≥4. Explicit expressions of the identities are obtained for n\phantom\rule0ex0ex=\phantom\rule0ex0ex4. It is also shown that the identities provide the missing link needed for a complete determination of the duality relation for the n-point boundary correlation function. The n\phantom\rule0ex0ex=\phantom\rule0ex0ex4 duality relation is obtained explicitly. More generally we deduce the number of sum rule identities as well as a cyclic inversion relation for any n, and conjecture on the general form of the duality relation.

Citations

• Duality relations for Potts correlation functions
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Some generalized order-disorder transformations
• A Determinant Formula for the Number of Ways of Coloring a Map