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 TMF, 2000, Volume 123, Number 1, Pages 116–131 (Mi tmf591)

Singular points of time-dependent correlation functions of spin systems on large-dimensional lattices at high temperatures

V. E. Zobov

L. V. Kirensky Institute of Physics, Siberian Branch of the Russian Academy of Sciences

Abstract: Time-dependent autocorrelation functions are investigated for the Heisenberg model with spins 1/2 on $d$-dimensional simple cubic lattices of large dimensions $d$ at infinite temperature. The autocorrelation function on the imaginary time axis is interpreted as the generating function of bond trees constructed with double bonds. These trees provide the leading terms with respect to $1/d$ for the time-expansion coefficients of the autocorrelation function. The correction terms from branch intersections to the generating function in the Bethe approximation are derived for these trees. A procedure is suggested for finding the correction to the coordinate of the singular point of the generating function (i.e., to the reciprocal of the branch growth-rate parameter) from the above correction terms without calculating the number of trees. The leading correction terms of order $1/\sigma^2$ (where $\sigma=2d-1$) are found for the coordinates of the singular points of the autocorrelation function in question and for the generating function of the trees constructed with single bonds in the Eden model.

DOI: https://doi.org/10.4213/tmf591

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English version:
Theoretical and Mathematical Physics, 2000, 123:1, 511–523

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Revised: 30.09.1999

Citation: V. E. Zobov, “Singular points of time-dependent correlation functions of spin systems on large-dimensional lattices at high temperatures”, TMF, 123:1 (2000), 116–131; Theoret. and Math. Phys., 123:1 (2000), 511–523

Citation in format AMSBIB
\Bibitem{Zob00} \by V.~E.~Zobov \paper Singular points of time-dependent correlation functions of spin systems on large-dimensional lattices at high temperatures \jour TMF \yr 2000 \vol 123 \issue 1 \pages 116--131 \mathnet{http://mi.mathnet.ru/tmf591} \crossref{https://doi.org/10.4213/tmf591} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1773215} \zmath{https://zbmath.org/?q=an:0968.82012} \transl \jour Theoret. and Math. Phys. \yr 2000 \vol 123 \issue 1 \pages 511--523 \crossref{https://doi.org/10.1007/BF02551058} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000087532100011} 

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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, “A Monte Carlo study of the dependence of the growth parameter for trees on the lattice dimension in the Eden model”, Theoret. and Math. Phys., 126:2 (2001), 270–279
2. 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”, Theoret. and Math. Phys., 131:3 (2002), 862–872
3. 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
4. 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
5. V. E. Zobov, M. A. Popov, “Tree Growth Parameter in the Eden Model on Face-Centered Hypercubic Lattices”, Theoret. and Math. Phys., 144:3 (2005), 1361–1371
6. V. E. Zobov, “The critical exponent of the tree lattice generating function in the Eden model”, Theoret. and Math. Phys., 165:2 (2010), 1443–1455
7. Bouch G., “Complex-Time Singularity and Locality Estimates For Quantum Lattice Systems”, J. Math. Phys., 56:12 (2015), 123303
8. 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
9. V. E. Zobov, M. M. Kucherov, “On the effect of an inhomogeneous magnetic field on high-frequency asymptotic behaviors of correlation functions of spin lattices”, JETP Letters, 107:9 (2018), 553–557
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