New order parameters in the Potts model on a Cayley tree

Details New order parameters in the Potts model on a Cayley tree New order parameters in the Potts model on a Cayley tree

2001-10-15

arxiv.org/abs/cond-mat/0110286v1

Physics

Condensed Matter

Statistical Mechanics

16 pages TeX, 5 figures PostScript

Scientific paper

10.1088/0305-4470/34/50/308

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.

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