Optimal Gaussian approximation in the fluctuating field theory

N. B. Melnikov ; B. I. Reser

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. II, Tome 271 (2010), pp. 159-180

Résumé

We consider the problem of calculating the partition function given by the functional integral over an external field that fluctuates in space and in “time” $\tau\in[0,1/T]$ ($T$ is temperature). A method is presented for calculating such integrals with the help of the Gaussian approximation that takes into account dynamics and non-locality of the fluctuations. The method is based on the free energy minimum principle.

Bibliographie

[1] Moriya T., Spinovye fluktuatsii v magnetikakh s kollektivizirovannymi elektronami, Mir, M., 1988

[2] Stratonovich R.L., “Ob odnom metode vychisleniya kvantovykh funktsii raspredeleniya”, DAN SSSR, 115:6 (1957), 1097–1100 | Zbl

[3] Hubbard J., “Calculation of partition functions”, Phys. Rev. Lett., 3:2 (1959), 77–78 | DOI | MR

[4] Feynman R.P., “Slow electrons in a polar crystal”, Phys. Rev., 97 (1955), 660–665 | DOI | Zbl

[5] Hertz J.A., Klenin M.A., “Fluctuations in itinerant-electron paramagnets”, Phys. Rev. B, 10:3 (1974), 1084–1096 | DOI

[6] Hertz J.A., Klenin M.A., “Sloppy spin waves above $T_\mathrm {C}$”, Physica B+C, 91 (1977), 49–55 | DOI

[7] Rezer B.I., Grebennikov V.I., “Raschet plotnosti sostoyanii i namagnichennosti ferromagnitnykh metallov s uchetom lokalnykh spinovykh fluktuatsii”, FMM, 83:2 (1997), 29–40

[8] Rezer B.I., Grebennikov V.I., “Temperaturnaya zavisimost magnitnykh svoistv ferromagnitnykh metallov s uchetom dinamiki i nelokalnosti spinovykh fluktuatsii”, FMM, 85:1 (1998), 30–42

[9] Hubbard J., “The magnetism of iron”, Phys. Rev. B, 19:5 (1979), 2626–2636 | DOI

[10] Grebennikov V.I., Prokopev Yu.I., Sokolov O.B., Turov E.A., “Metod lokalnykh fluktuatsii v teorii magnetizma perekhodnykh metallov”, FMM, 52:4 (1981), 679–694 | Zbl

[11] Reser B.I., Melnikov N.B., Grebennikov V.I., “Beyond Gaussian approximation in the spin-fluctuation theory of metallic ferromagnetism”, J. Phys.: Conf. Ser., 200 (2010), Pap. 012163 | DOI

[12] Melnikov N.B., Reser B.I., Grebennikov V.I., “Spin-fluctuation theory beyond Gaussian approximation”, J. Phys. A: Math. and Theor., 43:19 (2010), Pap. 195004 | DOI

[13] Kakehashi Y., “Dynamical coherent-potential approximation to the magnetism in a correlated electron system”, Phys. Rev. B, 65:18 (2002), Pap. 184420 | DOI

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

[15] Medvedev B.V., Nachala teoreticheskoi fiziki, 2-e izd., Fizmatlit, M., 2007 | Zbl

[16] Ryder L.H., Quantum Field Theory, 2nd ed., Cambridge Univ. Press, Cambridge, 1996 ; Райдер Л., Квантовая теория поля, Мир, М, 1987 | MR | Zbl

[17] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989 | MR

[18] Tyablikov S.V., Metody kvantovoi teorii magnetizma, 2-e izd., Nauka, M., 1975 | MR

[19] Bogolyubov N.N., Shirkov D.V., Vvedenie v teoriyu kvantovannykh polei, 4-e izd., Nauka, M., 1984 | MR

[20] White R.M., Quantum theory of magnetism: Magnetic properties of materials, 3rd ed., Springer, Berlin, 2007

[21] Bruus H., Flensberg K., Many-body quantum theory in condensed matter physics: An introduction, Oxford Univ. Press, Oxford, 2004

[22] Melnikov N.B., Reser B.I., Grebennikov V.I., “Dynamic spin-fluctuation theory beyond Gaussian approximation with application to iron”, Solid State Phenom., 2010, To appear

[23] Reser B.I., Melnikov N.B., “Problem of temperature dependence in the dynamic spin-fluctuation theory for strong ferromagnets”, J. Phys.: Condens. Matter., 20:28 (2008), Pap. 285205 | DOI | MR