Geodesic
Correlation functions of the semi-infinite two-dimensional ising model. II. Two-point correlation functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 2, pp. 262-270 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The two-point correlations formed by spin and energy-density operators are calculated exactly for the semi-infinite two-dimensional Ising model. It is shown that these correlations have a scaling form near the critical point. The asymptotic behaviour of the scaling functions is studied for various distances and configurations of operators on the lattice. The results obtained are used for the verification of the phenomenological theories: the decay of correlations and scaling. On the basis of the exact results the phenomenological rule for calculating the asymptotics of the correlation functions is proposed for the case when the distance between one of the operators and the boundary is much smaller than the distance between the operators. Using this rule, the dependence of the local thermodynamic functions on the distance from the boundary is obtained. 
@article{TMF_1980_42_2_a10,
     author = {R. Z. Bariev},
     title = {Correlation functions of~the semi-infinite two-dimensional ising model. {II.~Two-point} correlation functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {262--270},
     year = {1980},
     volume = {42},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_42_2_a10/}
}
TY  - JOUR
AU  - R. Z. Bariev
TI  - Correlation functions of the semi-infinite two-dimensional ising model. II. Two-point correlation functions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1980
SP  - 262
EP  - 270
VL  - 42
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1980_42_2_a10/
LA  - ru
ID  - TMF_1980_42_2_a10
ER  - 
%0 Journal Article
%A R. Z. Bariev
%T Correlation functions of the semi-infinite two-dimensional ising model. II. Two-point correlation functions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1980
%P 262-270
%V 42
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1980_42_2_a10/
%G ru
%F TMF_1980_42_2_a10
R. Z. Bariev. Correlation functions of the semi-infinite two-dimensional ising model. II. Two-point correlation functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 2, pp. 262-270. http://geodesic.mathdoc.fr/item/TMF_1980_42_2_a10/

[1] R. Z. Bariev, TMF, 40 (1979), 95 | MR

[2] W. J. Camp, M. E. Fisher, Phys. Rev., B6 (1972), 946 | DOI

[3] L. P. Kadanoff, Nuovo Cim., B44 (1966), 276 | DOI

[4] T. T. Wu, Phys. Rev., 149 (1966), 380 | DOI

[5] R. Hecht, Phys. Rev., 158 (1967), 557 | DOI

[6] A. M. Polyakov, ZhETF, 55 (1968), 1026; 57 (1969), 271

[7] G. Benettin, G. Jona-Lasinio, A. Stella, Let. Nuovo Cim., 4 (1973), 443 | DOI

[8] M. Fisher, Ustoichivost i fazovye perekhody, Sb., «Mir», 1973 | MR

[9] K. Binder, P. C. Hohenberg, Phys. Rev., B6 (1972), 3461 | DOI

[10] M. N. Barber, Phys. Rev., B8 (1973), 407 | DOI

[11] T. C. Lubensky, M. H. Rubin, Phys. Rev., B11 (1975), 4533 | DOI

[12] A. J. Bray, M. A. Moore, J. Phys., A10 (1977), 1927 | MR

[13] B. M. McCoy, T. T. Wu, Phys. Rev., 162 (1967), 436 | DOI | MR

[14] D. B. Abraham, Studies Appl. Math., 50 (1971), 71 | DOI | MR

[15] L. N. Karmazina, E. A. Chistova, Tablitsy funktsii Besselya ot mnimogo argumenta i integralov ot nikh, Izd-vo AN SSSR, 1958 | MR

[16] P. Reed, J. Phys., A11 (1978), 137

[17] R. Z. Bariev, Physica, A93 (1978), 354 | DOI

[18] A. Z. Patashinskii, V. L. Pokrovskii, Fluktuatsionnaya teoriya fazovykh perekhodov, «Nauka», 1975 | MR

[19] L. P. Kadanov, Kvantovaya teoriya polya i fizika fazovykh perekhodov, Sb., «Mir», 1975