The Ising model in two dimensions is a type of dependent site percolation model which is characterized by
the existence of a random variable 
assigning to each point 
a value of 
and is described on a finite
region 
by a probability distribution of the
form
 |
where 
is the normalizing constant,
, and the sum
is over interacting site pairs. Each spin random variable 
takes values in 
.
Some authors differentiate between positive (or ferromagnetic) dependency and negative (or antiferromagnetic) dependency
(Newman 1990) depending on the sign of the quantity 
, though little mention of this
distinction appears overall.
Other examples of dependent percolation models include the Potts models-generalizations of the Ising model in which 
is allowed to take on 
different values rather than the usual two-and the random-cluster model.
On the infinite 
-regular tree with 
, the free zero-field ferromagnetic Gibbs
measure with unit coupling at inverse temperature 
is also the broadcast process with a uniform root
spin and independent edge
transmissions having correlation 
.
