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TMF, 2003, Volume 136, Number 3, Pages 463–479 (Mi tmf237)  

This article is cited in 9 scientific papers (total in 9 papers)

The Coordinate of the Singular Point of Generating Functions of Clusters in the High-Temperature Dynamics of Spin Lattice Systems with Axially Symmetric Interaction

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: We investigate generating functions for equipped trees composed of double bonds of two sorts on a hypercubic lattice of dimension $d$ with built-in fragments. Rules for constructing these clusters are chosen to ensure the estimate for coefficients of power series in time for the longitudinal and transverse autocorrelation functions of the spin system with axially symmetric interaction. We derive a system of two equations for the tree-generating functions and an equation for the generating functions of chains leading from the root to a fragment in a tree using the Bethe approximation and under the condition that mainly bonds of one sort are taken into account. For the face-centered hypercubic lattice, we find the first terms of the $1/d$ expansion for the coordinate of the singular point of the generating function in both the anisotropic and the isotropic cases taking fragments in the forms of a triangle from four bonds and a four-fold bound pair into account. The obtained result is written in terms of ratios of lattice sums and is generalized to nuclear spin systems with dipole-dipole interaction. The theoretical value of the singular-point coordinate agrees well with the experimental value calculated from the tail of the absorption spectrum of the nuclear magnetic resonance in a barium fluoride monocrystal.

Keywords: spin dynamics, singular points, expansion over the reciprocal space dimension

DOI: https://doi.org/10.4213/tmf237

Full text: PDF file (276 kB)
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English version:
Theoretical and Mathematical Physics, 2003, 136:3, 1297–1311

Bibliographic databases:

Received: 23.07.2002
Revised: 12.02.2003

Citation: 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”, TMF, 136:3 (2003), 463–479; Theoret. and Math. Phys., 136:3 (2003), 1297–1311

Citation in format AMSBIB
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\by V.~E.~Zobov, M.~A.~Popov
\paper The Coordinate of the Singular Point of Generating Functions of Clusters in the High-Temperature Dynamics of Spin Lattice Systems with Axially Symmetric Interaction
\jour TMF
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\vol 136
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\pages 463--479
\mathnet{http://mi.mathnet.ru/tmf237}
\crossref{https://doi.org/10.4213/tmf237}
\zmath{https://zbmath.org/?q=an:1178.82052}
\transl
\jour Theoret. and Math. Phys.
\yr 2003
\vol 136
\issue 3
\pages 1297--1311
\crossref{https://doi.org/10.1023/A:1025603416535}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. E. Zobov, A. A. Lundin, “Modeling Multiparticle Coherences in Solid-State Nuclear Spin Systems Using Infinite-Range Interaction”, Theoret. and Math. Phys., 141:3 (2004), 1737–1749  mathnet  crossref  crossref  adsnasa  isi
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Zobov VE, Popov MA, “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), 775–783  crossref  adsnasa  isi  scopus  scopus
    4. Zobov, VE, “Second moment of multiple-quantum NMR and a time-dependent growth of the number of multispin correlations in solids”, Journal of Experimental and Theoretical Physics, 103:6 (2006), 904  crossref  adsnasa  isi  scopus  scopus
    5. Zobov, VE, “On the Second Moment of the Multiquantum NMR Spectrum of a Solid”, Russian Journal of Physical Chemistry B, 2:5 (2008), 676  crossref  isi  scopus  scopus
    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  mathnet  crossref  crossref  isi
    7. 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  mathnet  crossref  crossref  isi  elib
    8. 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  mathnet  crossref  crossref  isi  elib  elib
    9. 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  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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