Abstract:
A nonlinear integrodifferential equation is derived for the autocorrelation function of the Heisenberg paramagnet at high temperatures in the limit of an infinite-dimensional lattice. The solution of this equation on the plane of the complex time variable is investigated. A majorant and a minorant for the autocorrelation function on the imaginary axis are found, together with the nearest singular points. It is shown that at high frequencies the spectral density decreases exponentially. The damping constant and the pre-exponential factor are determined by the method of moments. The moments to tenth order are calculated.
Citation:
V. E. Zobov, “Autocorrelation function of a Heisenberg paramagnet in the approximation of a self-consistent fluctuating field”, TMF, 77:3 (1988), 426–439; Theoret. and Math. Phys., 77:3 (1988), 1299–1309
\Bibitem{Zob88}
\by V.~E.~Zobov
\paper Autocorrelation function of a Heisenberg paramagnet in the approximation of a self-consistent fluctuating field
\jour TMF
\yr 1988
\vol 77
\issue 3
\pages 426--439
\mathnet{http://mi.mathnet.ru/tmf6115}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=982417}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 77
\issue 3
\pages 1299--1309
\crossref{https://doi.org/10.1007/BF01016985}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1988AK72200010}
Linking options:
https://www.mathnet.ru/eng/tmf6115
https://www.mathnet.ru/eng/tmf/v77/i3/p426
This publication is cited in the following 18 articles:
Zobov V.E. Kucherov M.M., “Exponential Bound For the Heating Rate of Periodically Driven Spin Systems”, J. Exp. Theor. Phys., 128:4 (2019), 641–649
V. E. Zobov, M. M. Kucherov, “Concentration dependence of the wings of a dipole-broadened magnetic resonance line in magnetically diluted lattices”, J. Exp. Theor. Phys., 124:1 (2017), 151
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
Bouch G., “Complex-Time Singularity and Locality Estimates For Quantum Lattice Systems”, J. Math. Phys., 56:12 (2015), 123303
A. A. Lundin, V. E. Zobov, “Order dependence of the profile of the intensities of multiple-quantum coherences”, J. Exp. Theor. Phys., 120:5 (2015), 762
Dmitry A. Abanin, Wojciech De Roeck, François Huveneers, “Exponentially Slow Heating in Periodically Driven Many-Body Systems”, Phys. Rev. Lett., 115:25 (2015)
A. G. Lundin, V. E. Zorin, “Nuclear magnetic resonance in condensed matter”, Phys. Usp., 50:10 (2007), 1053–1077
Zobov, VE, “The coordinate of a singular point of the time correlation functions for a heteronuclear spin system of a crystal”, Journal of Experimental and Theoretical Physics, 100:4 (2005), 775
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
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
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
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
V. E. Zobov, A. A. Lundin, O. E. Rodionova, “The shape of NMR absorption and cross-relaxation spectra in a heteronuclear spin system”, J. Exp. Theor. Phys., 93:3 (2001), 542
V. E. Zobov, “Singular points of time-dependent correlation functions of spin systems on large-dimensional lattices at high temperatures”, Theoret. and Math. Phys., 123:1 (2000), 511–523
Zobov, VE, “Orientational dependence of the tails of dipole-broadened NMR spectra in crystals”, Journal of Experimental and Theoretical Physics, 88:1 (1999), 157
V. E. Zobov, M. A. Popov, “On convergence radius of time-power series for spin correlation functions of the Heisenberg magnet at high temperature”, Theoret. and Math. Phys., 112:3 (1997), 1182–1191
V. E. Zobov, M. A. Popov, “Dynamics of a system with three-spin interection in the Gaussian fluctuating local field approximation”, Theoret. and Math. Phys., 102:2 (1995), 224–234
V. E. Zobov, “Autocorrelation functions of the anisotropic Heisenberg paramagnet in the approximation of a self-consistent fluctuating field”, Theoret. and Math. Phys., 84:1 (1990), 751–757
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