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 Num. Meth. Prog., 2014, Volume 15, Issue 3, Pages 461–475 (Mi vmp264)

A renormalized Gaussian approximation in the spin-fluctuation theory

N. B. Melnikov, G. V. Paradezhenko

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: 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.

Full text: PDF file (376 kB)
UDC: 517.97:51-72:519.677:537.9

Citation: N. B. Melnikov, G. V. Paradezhenko, “A renormalized Gaussian approximation in the spin-fluctuation theory”, Num. Meth. Prog., 15:3 (2014), 461–475

Citation in format AMSBIB
\Bibitem{MelPar14} \by N.~B.~Melnikov, G.~V.~Paradezhenko \paper A renormalized Gaussian approximation in the spin-fluctuation theory \jour Num. Meth. Prog. \yr 2014 \vol 15 \issue 3 \pages 461--475 \mathnet{http://mi.mathnet.ru/vmp264} 

• http://mi.mathnet.ru/eng/vmp264
• http://mi.mathnet.ru/eng/vmp/v15/i3/p461

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This publication is cited in the following articles:
1. N. B. Melnikov, G. V. Paradezhenko, “Magnetic phase transitions in spin-fluctuation theory”, Theoret. and Math. Phys., 183:3 (2015), 868–877