Sie befinden Sich nicht im Netzwerk der Universität Paderborn. Der Zugriff auf elektronische Ressourcen ist gegebenenfalls nur via VPN oder Shibboleth (DFN-AAI) möglich.
mehr Informationen...
We consider the
Q-state Potts model in the random-cluster formulation, defined on
finite two-dimensional lattices of size
L
×
N
with toroidal boundary conditions. Due to the non-locality of the clusters, the partition function
Z
(
L
,
N
)
cannot be written simply as a trace of the transfer matrix
T
L
. Using a combinatorial method, we establish the decomposition
Z
(
L
,
N
)
=
∑
l
,
D
k
b
(
l
,
D
k
)
K
l
,
D
k
, where the characters
K
l
,
D
k
=
∑
i
(
λ
i
)
N
are simple traces. In this decomposition, the amplitudes
b
(
l
,
D
k
)
of the eigenvalues
λ
i
of
T
L
are labelled by the number
l
=
0
,
1
,
…
,
L
of clusters which are non-contractible with respect to the transfer (
N) direction, and a representation
D
k
of the cyclic group
C
l
. We obtain rigorously a general expression for
b
(
l
,
D
k
)
in terms of the characters of
C
l
, and, using number theoretic results, show that it coincides with an expression previously obtained in the continuum limit by Read and Saleur.