Many models of this type come about naturally in a number of fields. For example, a popular tool in statistical mechanics is the two-dimensional Ising
model, a type of dependent site percolation
model used to study the dipole moments of magnetic spins. Other examples 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.

Ostensibly, it would also make sense to talk about dependent percolation models in contexts such as -dimensional
discrete percolation theory for arbitrary , as well as in continuum percolation theory; even so, the
literature on such generalizations is scarce at best.