Summary: Notes on the cluster expansion for the polymer gas,
a.k.a., the Mayer expansion
Let be the finite set of lattice sites in Zd
. Any nonempty subset Y
is called a polymer. We denote by P() the set of all such polymers. On the
complex space CP()
we consider the polynomial (in fact multiaffine) function
Z defined by
Z(z) =
p0
1
p!
Y1,...,YpP()
1l
the Yi are
disjoint
z(Y1) . . . z(Yp)
for any z = (z(Y ))Y P() in CP()
. The variable z(Y ) is called the activity of
the the polymer Y . The purpose of this section is to give an explicit formula for

Source: Abdesselam, Abdelmalek - Department of Mathematics, University of Virginia

Collections: Mathematics