In statistical mechanics, the two-dimensional Ising model is a popular tool used to study the dipole moments of magnetic spins.
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 driven by a distribution 
of the form
 |
where 
is a real constant, 
, and 
for site random variables 
, 
.
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.
