Geodesic
Self-consistent field near the critical point in the Ising antiferromagnetic model
Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 2, pp. 244-253 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

On the basis of physical considerations, a class of diagrams governing the thermodynamic behavior of the fsing antiferromagnetic and ferromagnetic models in the critical domain for $T ($T_{\text к}$ is the critical temperature) for the case of nearest neighbor interaction is mentioned. The nature of the singularity for antiferromagnetic susceptibility is determined by summing these diagrams, and also for the polarization, specific heat, and susceptibility in the ferromagnetic case. The domain of critical behavior $z^{-2}<(T_{\text к}-T)/T_{\text к} ($z$ is the number of nearest neighbors) is also determined for the ferromagnetic case. A method is mentioned for reconstructing the diagram series to permit a correct determination of the critical temperature. Summation of the diagrams results in a transcendental equation, and specific results are obtained by solving it numerically. The volume of calculations needed to compute the critical behavior in the proposed method is considerably less than for computations based on an analysis of high- and low-temperature expansions. The results obtained agree with experimental results and with those found numerically. 
@article{TMF_1970_2_2_a6,
     author = {V. Ya. Krivnov and O. A. Ol'khov and B. N. Provotorov and M. E. Sarychev},
     title = {Self-consistent field near the critical point in the {Ising} antiferromagnetic model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {244--253},
     year = {1970},
     volume = {2},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1970_2_2_a6/}
}
TY  - JOUR
AU  - V. Ya. Krivnov
AU  - O. A. Ol'khov
AU  - B. N. Provotorov
AU  - M. E. Sarychev
TI  - Self-consistent field near the critical point in the Ising antiferromagnetic model
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1970
SP  - 244
EP  - 253
VL  - 2
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1970_2_2_a6/
LA  - ru
ID  - TMF_1970_2_2_a6
ER  - 
%0 Journal Article
%A V. Ya. Krivnov
%A O. A. Ol'khov
%A B. N. Provotorov
%A M. E. Sarychev
%T Self-consistent field near the critical point in the Ising antiferromagnetic model
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1970
%P 244-253
%V 2
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1970_2_2_a6/
%G ru
%F TMF_1970_2_2_a6
V. Ya. Krivnov; O. A. Ol'khov; B. N. Provotorov; M. E. Sarychev. Self-consistent field near the critical point in the Ising antiferromagnetic model. Teoretičeskaâ i matematičeskaâ fizika, Tome 2 (1970) no. 2, pp. 244-253. http://geodesic.mathdoc.fr/item/TMF_1970_2_2_a6/

[1] R. Braut, Fazovye perekhody, «Mir», 1967

[2] M. Fisher, Priroda kriticheskogo sostoyaniya, «Mir», 1968

[3] M. E. Fisher, M. F. Sykes, Physica, 28 (1962), 939 | DOI

[4] C. A. Hurst, H. S. Green, J. Chem. Phys., 33 (1960), 1059 | DOI | MR

[5] A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinskii, Metody kvantovoi teorii polya v statisticheskoi fizike, Fizmatgiz, 1962 | MR | Zbl

[6] C. Bloch, C. de Dominicis, Nucl. Phys., 7 (1958), 459 | DOI | Zbl

[7] V. Ya. Krivnov, O. A. Olkhov, B. N. Provotorov, ZhETF, 54 (1968), 456

[8] V. G. Vaks, A. I. Larkin, S. A. Pikin, ZhETF, 51 (1966), 361

[9] V. L. Pokrovskii, UFN, 1 (1968), 127 | DOI

[10] V. M. Zadvernyuk, V. Ya. Krivnov, FTT, 10 (1968), 188

[11] J. M. Luttinger, J. C. Ward, Phys. Rev., 118 (1960), 1147 | DOI | MR

[12] Yu. G. Rudoi, DAN SSSR, 174 (1967), 316

[13] M. A. Lasheen, I. Van den Brock, G. I. Gorter, Physica, 24 (1958), 1061 | DOI