  For the $q-$state Potts model new order parameters projecting on a group of
spins instead of a single spin are introduced. On a Cayley tree this allows the
physical interpretation of the Potts model at noninteger values q of the number
of states. The model can be solved recursively. This recursion exhibits chaotic
behaviour changing qualitatively at critical values of $q_0$ . Using an
additional order parameter belonging to a group of zero extrapolated size the
additional ordering is related to a percolation problem. This percolation
distinguishes different phases and explains the critical indices of percolation
class occuring at the Peierls temperature.
