| Sumari: | For Potts model on a Cayley tree we produce recursive relations that provide us the numerically exact phase diagram of the model. Each phase is characterized by a
particular attractor and the phase diagram is obtained by following the evolution and detecting the qualitative changements of these attractors. These changements can be
either continuous or abrupt, respectively characterizing second- or first- order phase transitions. We present a few typical attractors and at finite temperatures, several
interesting features (evolution of reentrances, separation of the modulated region into few disconnected pieces, etc) are exhibited for typical values of parameters.
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