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 TMF, 2002, Volume 131, Number 3, Pages 491–502 (Mi tmf342)

On the Coordinate of a Singular Point of the Time Correlation Function for a Spin System on a Simple Hypercubic Lattice at High Temperatures

V. E. Zobova, M. A. Popovb

a L. V. Kirensky Institute of Physics, Siberian Branch of the Russian Academy of Sciences
b Krasnoyarsk State University

Abstract: Using the $d^{-1}$ expansion method ($d$ is the space dimension), we estimate the coordinate of the time-dependent autocorrelation function singular point on the imaginary time axis for the spin 1/2 Heisenberg model on a simple hypercubic lattice at high temperatures. We represent the coefficients of the time expansion (the spectral moments) for the autocorrelation function as the sums of the weighted lattice figures in which the trees constructed from the double bonds give the leading contributions with respect to $d^{-1}$ and the same trees with the built-in squares from six bonds or diagrams with the fourfold bonds give the contribution of the next-to-leading order. We find the corrections to the coordinate of the autocorrelation function singular point that are due to the latter contributions.

DOI: https://doi.org/10.4213/tmf342

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English version:
Theoretical and Mathematical Physics, 2002, 131:3, 862–872

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Revised: 25.10.2001

Citation: V. E. Zobov, M. A. Popov, “On the Coordinate of a Singular Point of the Time Correlation Function for a Spin System on a Simple Hypercubic Lattice at High Temperatures”, TMF, 131:3 (2002), 491–502; Theoret. and Math. Phys., 131:3 (2002), 862–872

Citation in format AMSBIB
\Bibitem{ZobPop02} \by V.~E.~Zobov, M.~A.~Popov \paper On the Coordinate of a~Singular Point of the Time Correlation Function for a~Spin System on a~Simple Hypercubic Lattice at High Temperatures \jour TMF \yr 2002 \vol 131 \issue 3 \pages 491--502 \mathnet{http://mi.mathnet.ru/tmf342} \crossref{https://doi.org/10.4213/tmf342} \zmath{https://zbmath.org/?q=an:1031.82030} \transl \jour Theoret. and Math. Phys. \yr 2002 \vol 131 \issue 3 \pages 862--872 \crossref{https://doi.org/10.1023/A:1015935809388} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000176741900009} 

• http://mi.mathnet.ru/eng/tmf342
• https://doi.org/10.4213/tmf342
• http://mi.mathnet.ru/eng/tmf/v131/i3/p491

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. E. Zobov, M. A. Popov, “The Coordinate of the Singular Point of Generating Functions of Clusters in the High-Temperature Dynamics of Spin Lattice Systems with Axially Symmetric Interaction”, Theoret. and Math. Phys., 136:3 (2003), 1297–1311
2. Zobov, VE, “On the coordinate of a singular point of time correlation functions for the system of nuclear magnetic moments of a crystal”, Journal of Experimental and Theoretical Physics, 97:1 (2003), 78
3. V. E. Zobov, M. M. Kucherov, “On the concentration dependence of wings of spectra of spin correlation functions of diluted Heisenberg paramagnets”, JETP Letters, 103:11 (2016), 687–691
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