On Ising Model with Four Competing Interactions on Cayley Tree

Nasir Ganikhodjaev1,2, U. A. Rozikov3
1International Islamic University Malaysia, Kuantan, Malaysia
2National University of Uzbekistan, Tashkent, Uzbekistan
3Institute of Mathematics and Information Technologies, Tashkent, Uzbekistan

Tóm tắt

Từ khóa


Tài liệu tham khảo

Baxter, R.J.: Exactly Solved Models in Statistical Mechanics. Academic, London (1982)

Bleher, P., Ruiz, J., Schonmann, R.H., Schlosman, S., Zagrebnov, V.: Rigidity of the critical phases on a Cayley tree. Moscow Math. J. 1, 345–363 (2001)

Bleher, P., Ruiz, J., Zagrebnov, V.: On the purity of the limiting Gibbs state for the Ising model on the Bethe lattice. J. Statist. Phys. 79, 473–482 (1995)

Bleher, P., Ganikhodjaev, N.: On the phases of the Ising model on the Bethe lattice. Theory Probab. Appl. 35, 216–227 (1990)

Ganikhodjaev, N.N.: Group representations and automophisms of the Cayley tree. Dokl. Akad. Nauk. Rep. Uzbekistan 4, 3–5 (1994) (Russian)

Ganikhodjaev (Ganikhodzhaev), N.N., Rozikov, U.A.: A description of periodic extremal Gibbs measures on some lattice models on the Cayley tree. Theor. Math. Phys. 111, 480–486 (1997)

Ganikhodjaev, N.N.: Exact solution of an Ising model on the Cayley tree with competing ternary and binary interactions. Theor. Math. Phys. 130(3), 419–424 (2002)

Ganikhodjaev, N.N., Pah, C.H., Wahiddin, M.R.B.: Exact solution of an Ising model with competing interactions on a Cayley tree. J. Phys. A 36, 4283–4289 (2003)

Ganikhodjaev, N.N., Pah, C.H., Wahiddin, M.R.B.: An Ising model with three competing interactions on a Cayley tree. J. Math. Phys. 45, 3645–3658 (2004)

Georgii, H.-O.: Gibbs Measures and Phase Transitions. Walte de Gruyter, Berlin (1998)

Katsura, S., Takizawa, M.: Bethe lattice and the Bethe approximation. Prog. Theor. Phys. 51, 82–98 (1974)

Kindermann, R., Snell, J.L.: Markov random fields and their applications. Contemp. Math. 1 (1980)

Korn, G.A., Korn, T.M.: Mathematical Handbook for Scientists and Engineers. McGraw-Hill, New York (1961)

Lyons, R.: Phase transitions on nonamenable group. J. Math. Phys. 41, 1099–1126 (2000)

Monroe, J.L.: Phase diagrams of Ising models on Husime trees II. J. Stat. Phys. 67, 1185–2000 (1992)

Monroe, J.L.: A new criterion for the location of phase transitions for spin system on a recursive lattice. Phys. Lett. A 188, 80–84 (1994)

Mukhamedov, F.M., Rozikov, U.A.: On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras. J. Statist. Phys. 114, 825–848 (2004)

Preston, K.: Gibbs States on Countable Sets. Cambridge, London (1974)

Rozikov, U.A.: Partition structures of the group representation of the Cayley tree into cosets by finite-index normal subgroups and their applications to description of periodic Gibbs distributions. Theor. Math. Phys. 112, 929–933 (1997)

Rozikov, U.A.: Description uncountable number of Gibbs measures for inhomogeneous Ising model. Theor. Math. Phys. 118, 95–104 (1999)

Shiryaev, A.N.: Probability. Nauka, Moscow (1980)

Sinai, Y.G.: Theory of Phase Transitions: Rigorous Results. Pergamon, Oxford (1982)

Spitzer, F.: Markov random field on infinite tree. Ann. Probab. 3, 387–398 (1975)

Suhov, Y.M., Rozikov, U.A.: A hard-core model on a Cayley tree: an example of a loss network. Queueing Systems 46, 197–212 (2004)