# zbMATH — the first resource for mathematics

On $$q$$-component models on the Cayley tree: the general case. (English) Zbl 1456.82096

##### MSC:
 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 82B23 Exactly solvable models; Bethe ansatz 82B26 Phase transitions (general) in equilibrium statistical mechanics
Full Text:
##### References:
 [1] Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (London: Academic) [2] Bleher P M and Ganikhodjaev N N 1990 On pure phases of the Ising model on the Bethe lattice Theor. Probab. Appl.35 216 · Zbl 0715.60122 [3] Borgs C 2004 Statistical physics expansion methods in combinatorics and computer science http://research.microsoft.com/∼borgs/CBMS.pdf [4] Fernández R 1998 Contour ensembles and the description of Gibbsian probability distributions at low temperature www.univ-rouen.fr/LMRS/persopage/Fernandez [5] Holsztynski W and Slawny J 1978 Peierls condition and the number of ground states Commun. Math. Phys.61 177 [6] Kashapov I A 1977 Structure of ground states in three-dimensional Ising model with tree-step interaction Theor. Math. Phys.33 912 [7] Minlos R A 2000 Introduction to Mathematical Statistical Physics(University Lecture Series vol 19) ISSN 1047-3998 [8] Mukhamedov F M and Rozikov U A 2004 On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras. I, II J. Stat. Phys.114 825 · Zbl 1061.82007 [9] Mukhamedov F M and Rozikov U A 2005 J. Stat. Phys.119 427 · Zbl 1071.82017 [10] Peierls R 1936 On Ising model of ferro magnetism Proc. Camb. Phil. Soc.32 477 · Zbl 0014.33604 [11] Pirogov S A and Sinai Ya G 1975 Phase diagrams of classical lattice systems, I Theor. Math. Phys.25 1185 [12] Pirogov S A and Sinai Ya G 1976 Theor. Math. Phys.26 39 [13] Rozikov U A and Suhov Yu M 2004 A hard-core model on a Cayley tree: an example of a loss network Queueing Syst.46 197 · Zbl 1139.90338 [14] Rozikov U A 2005 On q-component models on Cayley tree: contour method Lett. Math. Phys.71 27 · Zbl 1076.82509 [15] Rozikov U A 2006 A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree J. Stat. Phys.122 217 · Zbl 1149.82008 [16] Sinai Ya G 1982 Theory of Phase Transitions: Rigorous Results (Oxford: Pergamon) [17] Zahradnik M 1984 An alternate version of Pirogov-Sinai theory Commun. Math. Phys.93 559 [18] Zahradnik M 1998 A short course on the Pirogov-Sinai theory Rend. Math. Ser. VII 18 411 · Zbl 0927.60087
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.