Abstract:
The convergence of series in powers of time for spin autocorrelation functions of the Heisenberg magnet are investigated at infinite temperatures on lattices of different dimensions $d$. The calculation data available at the present time for the coefficients of these series are used to estimate the corresponding radii of convergence, whose growth with decreasing $d$ is revealed and explained in a self-consistent approximation. To this end, a simplified nonlinear equation corresponding to this approximation is suggested and solved for the autocorrelation function of a system with an arbitrary number $Z$ of nearest neighbors. The coefficients of the expansion in powers of time for the solution are represented in the form of trees on the Bethe lattice with the coordination number $Z$. A computer simulation method is applied to calculate the expansion coefficients for trees embedded in square, triangular, and simple cubic lattices under the condition that the intersection of tree branches is forbidden. It is found that the excluded volume effect that manifests itself in a decrease in these coefficients and in an increase in the coordinate and exponent of the singularity of the autocorrelation function on the imaginary time axis is intensified with decreasing lattice dimensions.
Citation:
V. E. Zobov, M. A. Popov, “On convergence radius of time-power series for spin correlation functions of the Heisenberg magnet at high temperature”, TMF, 112:3 (1997), 479–491; Theoret. and Math. Phys., 112:3 (1997), 1182–1191
\Bibitem{ZobPop97}
\by V.~E.~Zobov, M.~A.~Popov
\paper On convergence radius of time-power series for spin correlation functions of the Heisenberg magnet at high temperature
\jour TMF
\yr 1997
\vol 112
\issue 3
\pages 479--491
\mathnet{http://mi.mathnet.ru/tmf1057}
\crossref{https://doi.org/10.4213/tmf1057}
\transl
\jour Theoret. and Math. Phys.
\yr 1997
\vol 112
\issue 3
\pages 1182--1191
\crossref{https://doi.org/10.1007/BF02583049}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000071403900010}
Linking options:
https://www.mathnet.ru/eng/tmf1057
https://doi.org/10.4213/tmf1057
https://www.mathnet.ru/eng/tmf/v112/i3/p479
This publication is cited in the following 7 articles:
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
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
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, “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
Kim, J, “Dynamics of a harmonic oscillator on the Bethe lattice”, Physical Review E, 61:3 (2000), R2172
Zobov, VE, “Orientational dependence of the tails of dipole-broadened NMR spectra in crystals”, Journal of Experimental and Theoretical Physics, 88:1 (1999), 157
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