Ganikhodjaev, N. N.; Pah, C. H. Phase diagrams of multicomponent lattice models. (English) Zbl 1177.82043 Theor. Math. Phys. 149, No. 2, 1512-1518 (2006); translation from Teor. Mat. Fiz. 149, No. 224-251 (2006). Summary: We consider q-component models on both the integer lattice \(\mathbb Z^{2}\) and a second-order Cayley tree and study phase diagrams of these models. MSC: 82B26 Phase transitions (general) in equilibrium statistical mechanics 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics Keywords:Cayley tree; Gibbs measure; phase diagram PDF BibTeX XML Cite \textit{N. N. Ganikhodjaev} and \textit{C. H. Pah}, Theor. Math. Phys. 149, No. 2, 1512--1518 (2006; Zbl 1177.82043); translation from Teor. Mat. Fiz. 149, No. 224--251 (2006) Full Text: DOI References: [1] S. A. Pirogov and Ya. G. Sinai, Theor. Math. Phys., 25, 1185–1192 (1975). · doi:10.1007/BF01040127 [2] S. A. Pirogov and Ya. G. Sinai, Theor. Math. Phys., 26, 39–49 (1976). · doi:10.1007/BF01038255 [3] R. Peierls, Proc. Cambridge Philos. Soc., 32, 477–481 (1936). · Zbl 0014.33604 · doi:10.1017/S0305004100019174 [4] R. B. Griffiths, Phys. Rev. A, 136, 437–439 (1964). [5] P. L. Dobrushin, Theor. Probab. Appl., 10, 253–271 (1965). · Zbl 0168.23803 · doi:10.1137/1110026 [6] U. A. Rozikov, Lett. Math. Phys., 71, 27–38 (2005). · Zbl 1076.82509 · doi:10.1007/s11005-004-5117-2 [7] N. N. Ganikhodzhaev, Theor. Math. Phys., 130, 419–424 (2002). · Zbl 1031.82012 · doi:10.1023/A:1014771023960 [8] N. N. Ganikhodjaev, C. H. Pah, and M. R. B. Wahiddin, J. Phys. A, 36, 4283–4289 (2003). · Zbl 1168.82316 · doi:10.1088/0305-4470/36/15/305 [9] R. A. Minlos, Introduction to Mathematical Statistical Physics (University Lecture Series, Vol. 19), Amer. Math. Soc., Providence, R. I. (2000). · Zbl 0998.82501 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.