Editing Potts model (section)

=== Interacting model ===
The simplest case of the interacting model is the [[Ising model]], where the spin can only take on one of two values, ''s<sub>n</sub>'' ∈ {{mset|−1, 1}} and only nearest neighbor spins interact. The interaction potential is given by
: <math>V(\sigma) = -J_p s_0 s_1\,</math>

This potential can be captured in a 2 × 2 matrix with matrix elements
: <math>M_{\sigma \sigma'} = \exp \left( \beta J_p \sigma \sigma' \right)</math>
with the index σ, σ′ ∈ {−1, 1}.  The partition function is then given by
: <math>Z_n(V) = \mbox{Tr}\, M^n</math>

The general solution for an arbitrary number of spins, and an arbitrary finite-range interaction, is given by the same general form. In this case, the precise expression for the matrix ''M'' is a bit more complex.

The goal of solving a model such as the Potts model is to give an exact [[closed-form expression]] for the partition function and an expression for the [[Gibbs state]]s or [[equilibrium state]]s in the limit of ''n'' → ∞, the [[thermodynamic limit]].