The Q-state Potts model is a generalization of the Ising model to more-than-two components and has been a subject of an increasingly research interest over the last decades. An extended summary of results and a bibliography can be found in the review article by Wu [1] and references therein. The model has been studied on Bethe lattices also see [2-8]. The Bethe lattice is a topological abstaction compared to standard lattices. It corresponds to the interior of the infinitely extended Cayley tree with the coordination number γ. The surface of the Cayley tree cannot be neglected and leads to unusual behavior of models defined on a Cayley tree. However, under certain conditions, exact results on Bethe lattices correspond to approximate results on standard lattices. The fractal dimension of a Julia-set corresponding to a Yang-Lee zero of the partition function has also been studied [9].
[1] Wy, F. Y. The Potts Model, Rev. Mod. Phys 58 (1982)[2] de Aguiar and Goulart-Rosa, Phys. Lett. A. 162 (1992)[3] de Aguiar, Bernades and Goulart-Rosa, Jour. Stat. Phys. 64 (1991)[4] Wagner, Gensing and Heide, J. Phys. A: Math Gen 33 (2000)[5] Ananikyan and Akheyan: Zh. Eksp. Teor. Fiz 107 (1995)[6] Ghulghazaryan, Ananikyan and Sloot, Phys Rev E 66 (2002)[7] Peruggi, di Liberto and Monroy, J. Phys. A: Math Gen. 16 (1983)[8] di Leberto, Monroy and Peruggi, Z. Phys. B – Cond Matter 66 (1987)[9] Ghulghazaryan, Ananikyan and Jonassen: Springer Lecture Notes in Computer Science 2657 (2003)