Geodesic
A renormalized Gaussian approximation in the spin-fluctuation theory
Numerical methods and programming, Tome 15 (2014) no. 3, pp. 461-475.

Voir la notice de l'article provenant de la source Math-Net.Ru

The effect of spin fluctuations on the magnetic phase transition is studied by the functional integral method. The interaction between spin moments at finite temperatures is replaced by the interaction with a stochastic (fluctuating) field. Calculation of magnetic characteristics is reduced to the integration over the fluctuating field configurations in the Gaussian approximation. A characteristic feature of the Gaussian approximation is the first-order phase transition. In this paper a method is proposed for renormalizing the Gaussian approximation by taking into account the fourth-order terms of the free energy expansion in the fluctuating field. By the example of the Ising model, it is shown that the renormalization leads to the second-order phase transition, which is observed in experiments.
Keywords: functional integral method, Stratonovich-Hubbard transformation, Gaussian approximation, renormalization, trust-region method. 
@article{VMP_2014_15_3_a7,
     author = {N. B. Melnikov and G. V. Paradezhenko},
     title = {A renormalized {Gaussian} approximation in the spin-fluctuation theory},
     journal = {Numerical methods and programming},
     pages = {461--475},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2014_15_3_a7/}
}
TY  - JOUR
AU  - N. B. Melnikov
AU  - G. V. Paradezhenko
TI  - A renormalized Gaussian approximation in the spin-fluctuation theory
JO  - Numerical methods and programming
PY  - 2014
SP  - 461
EP  - 475
VL  - 15
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMP_2014_15_3_a7/
LA  - ru
ID  - VMP_2014_15_3_a7
ER  - 
%0 Journal Article
%A N. B. Melnikov
%A G. V. Paradezhenko
%T A renormalized Gaussian approximation in the spin-fluctuation theory
%J Numerical methods and programming
%D 2014
%P 461-475
%V 15
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMP_2014_15_3_a7/
%G ru
%F VMP_2014_15_3_a7
N. B. Melnikov; G. V. Paradezhenko. A renormalized Gaussian approximation in the spin-fluctuation theory. Numerical methods and programming, Tome 15 (2014) no. 3, pp. 461-475. http://geodesic.mathdoc.fr/item/VMP_2014_15_3_a7/