C. King
2D Potts model and annular partitions
(351K, Latex)
ABSTRACT. Using the random cluster expansion,
correlations of the Potts model on a graph can be expressed as
sums over partitions of
the vertices where the spins are fixed. For a planar graph,
only certain partitions can occur in these sums. For example,
when all fixed
spins lie on the boundary of one face, only noncrossing
partitions contribute. In this paper we examine the partitions
which occur
when fixed spins lie on the boundaries of two
disjoint faces. We call these the annular partitions,
and we establish some of their basic properties.
In particular we demonstrate a partial duality for these
partitions, and show some implications for correlations of the
Potts model.