Let 
be a finite graph, let 
be the set 
whose members are vectors 
, and let 
be the sigma-algebra
of all subsets of 
. A random-cluster model on 
is the measure 
on the measurable
space 
defined for each 
by
 |
(1)
|
where here, 
and 
are parameters, 
is the so-called partition function
 |
(2)
|
and 
denotes the number of connected components
of the graph 
where
 |
(3)
|
The connected components of 
are called open clusters.
In the above setting, the case 
corresponds to a model in which graph
edges are open (i.e., 
) or closed (i.e., 
) independently
of one another, a scenario which can be used as an alternative definition for the
term percolation. For cases 
, the random-cluster model models dependent
percolation.
