Geodesic
Linear transformation matrix for the correlation functions of the Ising model
Teoretičeskaâ i matematičeskaâ fizika, Tome 25 (1975) no. 2, pp. 280-288 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

New formulation of the Ising problem is given, according to which the solution of the problem is reduced to diagonalizing the matrix of a certain linear transformation $W$ in the space of vectors composed of the correlation functions of the model. The structure of the new operator differs in a principal way from that of the usual transfer matrix. The matrix $W$ has a higher order and, for example, in the case of planar lattices it splits into separate blocks which can be easily diagonalized and lead to the exact solution of the problem. 
@article{TMF_1975_25_2_a13,
     author = {R. Z. Bariev and M. P. Zhelifonov},
     title = {Linear transformation matrix for the correlation functions of the {Ising} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {280--288},
     year = {1975},
     volume = {25},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1975_25_2_a13/}
}
TY  - JOUR
AU  - R. Z. Bariev
AU  - M. P. Zhelifonov
TI  - Linear transformation matrix for the correlation functions of the Ising model
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1975
SP  - 280
EP  - 288
VL  - 25
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1975_25_2_a13/
LA  - ru
ID  - TMF_1975_25_2_a13
ER  - 
%0 Journal Article
%A R. Z. Bariev
%A M. P. Zhelifonov
%T Linear transformation matrix for the correlation functions of the Ising model
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1975
%P 280-288
%V 25
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1975_25_2_a13/
%G ru
%F TMF_1975_25_2_a13
R. Z. Bariev; M. P. Zhelifonov. Linear transformation matrix for the correlation functions of the Ising model. Teoretičeskaâ i matematičeskaâ fizika, Tome 25 (1975) no. 2, pp. 280-288. http://geodesic.mathdoc.fr/item/TMF_1975_25_2_a13/

[1] M. Kats, Ustoichivost i fazovye perekhody, «Mir», 1973, 241 | MR

[2] H. S. Green, C. A. Hurst, Order-Disorder Phenomena, Intercsience, London, 1964 | MR

[3] S. V. Tyablikov, V. K. Fedyanin, FMM, 23 (1967), 193

[4] M. P. Zhelifonov, TMF, 8 (1971), 401

[5] M. P. Zhelifonov, R. T. Galiullin, Phys. Lett., 42A (1973), 417 | DOI | MR

[6] R. T. Galiullin, M. P. Zhelifonov, B. S. Nikitin, TMF, 12 (1972), 147

[7] R. Z. Bariev, M. P. Zhelifonov, Phys. Lett., 42A (1972), 35 | DOI | MR

[8] R. Z. Bariev, M. P. Zhelifonov, Phys. Lett., 50A (1974), 105 | DOI | MR

[9] L. P. Kadanoff, Nuovo Cim., 44 (1966), 276 | DOI

[10] B. Kaufman, L. Onsager, Phys. Rev., 76 (1949), 1244 | DOI | Zbl