In this paper we consider Ising model on the semi-infinite Cayley tree of second order with left and right interaction and investigate the problem of phase transition for this model.
REFERENCES
1.
R. J.
Baxter
, Exactly solvable models in statistical mechanics
(Academic Press London
, New York
, 1982
).2.
R.
Bissacot
, and L. M.
Cioletti
, J. Stat. Phys.
139
(5
), 769
–778
(2010
).3.
P. M.
Bleher
, and N. N.
Ganikhodjaev
, Theory Probab. Appl.
35
, 216
–227
(1990
).4.
P. M.
Bleher
, J.
Ruiz
, and V.
Zagrebnov
, J. Stat. Phys.
93
, 33
–78
(1998
).5.
F. J.
Dyson
, Comm. Math. Phys.
12
, 91
–107
(1969
).6.
D.
Gandolfo
, M. M.
Rakhmatullaev
, U. A.
Rozikov
, and J.
Ruiz
, J. Stat. Phys.
150
(6
), 1201
–1217
(2013
).7.
D.
Gandolfo
, J.
Ruiz
, and S.
Shlosman
, J. Stat. Phys.
148
, 999
–1005
(2012
).8.
N. N.
Ganikhodjaev
, and U. A.
Rozikov
, Theor. Math. Phys.
111
, 480
–486
(1997
).9.
N. N.
Ganikhodjaev
, and U. A.
Rozikov
, Math. Phys., Anal. Geom.
12
, 141
–156
(2009
).10.
N. N.
Ganikhodjaev
, Theor. Math. Phys.
130
(3
), 419
–424
(2002
).11.
N. N.
Ganikhodjaev
, C. H.
Pah
, and M. R. B.
Wahiddin
, J. Phys. A
36
, 4283
–4289
(2003
).12.
N. N.
Ganikhodjaev
, C. H.
Pah
, and M. R. B.
Wahiddin
, J. Math. Phys.
45
, 3645
–3658
(2004
).13.
H.-O.
Georgii
, Gibbs Measures and Phase Transitions, Walter de Gruyter
, (de Gruyter Studies in Mathematics
, vol 9
), Berlin-New York
, 1988
.14.
R.
Kindermann
, and J. L.
Snell
, American Mathematical society, Providence
, 1980
.15.
C. J.
Preston
, Gibbs States on Countable Sets
(Cambridge University Press
, London
, 1974
).16.
U. A.
Rozikov
, Rev. Math. Phys.
, 25
(1
), 1330001
(2013
).17.
U. A.
Rozikov
, Gibbs measures on Cayley trees
(World Scientific Publishing
, Singapore
, 2013
).18.
Y. G.
Sinai
, Theory of Phase Transitions:Rigorous Results
(Pergamon Press
, Oxford
, 1982
).19.
F.
Spitzer
, Ann. Probab.
3
, 387
–398
(1975
).
This content is only available via PDF.
© 2016 Author(s).
2016
Author(s)
You do not currently have access to this content.
