New order parameters in the Potts model on a Cayley tree

Annotatsiya

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 q0 of the number of states. The model can be solved recursively. This recursion exhibits chaotic behaviour changing qualitatively at critical values of q0. 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.

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