Editing Potts model (section)

=== Free field solution ===
The simplest model is the model where there is no interaction at all, and so ''V'' = ''c'' and ''H<sub>n</sub>'' = ''c'' (with ''c'' constant and independent of any spin configuration).  The partition function becomes
: <math>Z_n(c) = e^{-c\beta} \sum_{s_0,\ldots,s_n \in Q} 1</math>

If all states are allowed, that is, the underlying set of states is given by a [[full shift]], then the sum may be trivially evaluated as
: <math>Z_n(c) = e^{-c\beta} q^{n+1}</math>

If neighboring spins are only allowed in certain specific configurations, then the state space is given by a [[subshift of finite type]]. The partition function may then be written as
: <math>Z_n(c) = e^{-c\beta} |\mbox{Fix}\, \tau^n| =  e^{-c\beta} \mbox{Tr} A^n</math>
where card is the [[cardinality]] or count of a set, and Fix is the set of [[Fixed point (mathematics)|fixed points]] of the iterated shift function:
: <math>\mbox{Fix}\, \tau^n =  \{ s \in Q^\mathbf{Z} : \tau^n s = s \}</math>

The ''q'' × ''q'' matrix ''A'' is the [[adjacency matrix]] specifying which neighboring spin values are allowed.