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On $$q$$-component models on Cayley tree: contour method. (English) Zbl 1076.82509
Summary: In the Letter we investigate a $$q$$-component models on a Cayley tree. The main goal of the Letter is to develop a “contour” argument on Cayley tree. We define contours and study some properties of these contours. Using a contour argument we show existence of $$q$$ different Gibbs measures for several $$q$$-component models.

##### MSC:
 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 82B05 Classical equilibrium statistical mechanics (general) 60K35 Interacting random processes; statistical mechanics type models; percolation theory 05C05 Trees
##### Keywords:
Cayley tree; configuration; Potts model; SOS model; contour; Gibbs measure
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##### References:
 [4] Fernández, R.: Contour ensembles and the description of Gibbsian probability distributions at low temperature. www.univ-rouen.fr/LMRS/persopage/Fernandez, 1998. [5] Fernández, R.: Contour ensembles and the description of Gibbsian probability distributions at low temperature. www.univ-rouen.fr/LMRS/persopage/Fernandez, 1998. [11] Minlos, R. A.: Introduction to Mathematical Statistical Physics, University lecture series, ISSN 1047-3998; v.19, 2000
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