Geodesic
Application of the functional integration method to the Heisenberg model of ferromagnetism
Teoretičeskaâ i matematičeskaâ fizika, Tome 5 (1970) no. 1, pp. 110-124 
Yu. A. Izyumov; Yu. N. Skryabin. Application of the functional integration method to the Heisenberg model of ferromagnetism. Teoretičeskaâ i matematičeskaâ fizika, Tome 5 (1970) no. 1, pp. 110-124. http://geodesic.mathdoc.fr/item/TMF_1970_5_1_a10/
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     title = {Application of the functional integration method to the {Heisenberg} model of ferromagnetism},
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The partition function of a Heisenberg ferromagnet is represented as a functional integral over the stochastic fields. The integrand describing the partition function of the system of spins without interaction is expanded in a series of powers of the stochastic fields. It is shown that this leads to the usual expansions of the original expression in powers of the interaction. A functional integral representation of the partition function in the Ising model is considered as a special case. By means of a cumulant expansion of the integrand a diagram technique is constructed for the calculation of the partition function, the magnetization, and the Green's functions of an Ising ferromagnet.

[1] E. S. Fradkin, DAN SSSR, 125 (1959), 66 | MR | Zbl

[2] E. S. Fradkin, Trudy FIAN, 29 (1965), 7 | Zbl

[3] E. S. Fradkin, Problemy teoreticheskoi fiziki, Sb., posvyaschennyi akad. N. N. Bogolyubovu v svyazi s ego shestidesyatiletiem, «Nauka», 1969, 386 | MR

[4] L. Ya. Kobelev, DAN SSSR, 180 (1968), 576

[5] M. Kac, E. Helfand, J. Math. Phys., 4 (1963), 1078 | DOI | MR | Zbl

[6] G. Beker, Phys. Rev., 126 (Phys. Rev.), 2071 | DOI

[7] E. S. Fradkin, DAN SSSR, 98 (1954), 47 | MR | Zbl

[8] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Gostekhizdat, 1957 | MR

[9] A. I. Akhiezer, V. B. Berestetskii, Kvantovaya elektrodinamika, «Nauka», 1969 | MR

[10] E. Gursa, Kurs matematicheskogo analiza, Tom 2, chast 2, GTTI, 1933

[11] Yu. A. Izyumov, F. A. Kassan-Ogly, FMM (to appear)