Abstract:
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.
Citation:
Yu. A. Izyumov, Yu. N. Skryabin, “Application of the functional integration method to the Heisenberg model of ferromagnetism”, TMF, 5:1 (1970), 110–124; Theoret. and Math. Phys., 5:1 (1970), 1018–1028
\Bibitem{IzySkr70}
\by Yu.~A.~Izyumov, Yu.~N.~Skryabin
\paper Application of the functional integration method to the Heisenberg model of ferromagnetism
\jour TMF
\yr 1970
\vol 5
\issue 1
\pages 110--124
\mathnet{http://mi.mathnet.ru/tmf4190}
\transl
\jour Theoret. and Math. Phys.
\yr 1970
\vol 5
\issue 1
\pages 1018--1028
\crossref{https://doi.org/10.1007/BF01035984}
Linking options:
https://www.mathnet.ru/eng/tmf4190
https://www.mathnet.ru/eng/tmf/v5/i1/p110
This publication is cited in the following 4 articles:
S.O Gladkov, “The kinetics of nuclear magnetically ordered systems”, Physics Reports, 182:4-5 (1989), 211
S.O. Gladkov, “On some kinetic phenomena in ordered and disordered substances”, Physics Reports, 152:2 (1987), 73
B. V. Moshchinskii, V. K. Fedyanin, “Asymptotic behavior of the Heisenberg model with long-range interaction”, Theoret. and Math. Phys., 31:1 (1977), 345–349
G. E. Gurgenishvili, G. A. Kharadze, “Application of the path-integration method to the s−d model of a metal with magnetic impurity”, Theoret. and Math. Phys., 11:1 (1972), 370–375
Citation in format AMSBIB
Contact us: