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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Popov M. A.
Заглавие : The coordinate of the singular point of generating functions of clusters in the high-temperature dynamics of spin lattice systems with axially symmetric interaction
Место публикации : Theor. Math. Phys.: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2003. - Vol. 136, Is. 3. - P1297-1311. - ISSN 0040-5779, DOI 10.1023/A:1025603416535
Примечания : Cited References: 25
Предметные рубрики: CONSISTENT FLUCTUATING FIELD
NUCLEAR-DOUBLE-RESONANCE
HEISENBERG PARAMAGNET
LINE SHAPE
RELAXATION
SPECTRUM
APPROXIMATION
CRYSTALS
MOMENT
CAF2
Ключевые слова (''Своб.индексиров.''): spin dynamics--singular points--expansion over the reciprocal space dimension--expansion over the reciprocal space dimension--singular points--spin dynamics
Аннотация: 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.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Popov M. A.
Заглавие : On the coordinate of a singular point of the time correlation function for a spin system on a simple hypercubic lattice at high temperatures
Место публикации : Theor. Math. Phys. - 2002. - Vol. 131, Is. 3. - P.862-872. - ISSN 0040-5779, DOI 10.1023/A:1015935809388
Примечания : Cited References: 19
Предметные рубрики: NUCLEAR-DOUBLE-RESONANCE
HEISENBERG MAGNET
DEPENDENCE
MODEL
Ключевые слова (''Своб.индексиров.''): spin dynamics--correlation functions--power series in time--frequency moments--singular points--generated functions--lattice trees--multidimensional expansion--correlation functions--frequency moments--generated functions--lattice trees--multidimensional expansion--power series in time--singular points--spin dynamics
Аннотация: 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.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Ivanov Y. N., Popov M. A., Livshits A. I.
Заглавие : Orientational dependence of the tails of dipole-broadened NMR spectra in crystals
Место публикации : J. Exp. Theor. Phys.: AMER INST PHYSICS, 1999. - Vol. 88, Is. 1. - P157-167. - ISSN 1063-7761, DOI 10.1134/1.558778
Примечания : Cited References: 36
Предметные рубрики: NUCLEAR-DOUBLE-RESONANCE
FLUCTUATION SPECTRUM
CROSS-RELAXATION
SOLIDS
DIFFUSION
MEMORY
SHAPE
Аннотация: This paper describes experimental and theoretical studies of the tails of the dipole-broadened nuclear magnetic resonance (NMR) absorption spectra of F-19 in isomorphic single crystals of BaF2 and CaF2 with the magnetic field directed along three crystallographic axes. The results obtained by directly measuring the derivative of the tail of the NMR absorption spectrum and the falloffs of the Engelsberg-Lowe free precession after Fourier transformation qualitatively agree. It is shown that the shape of the tail is well described by an exponential function in which the orientational dependence of the exponent does not reduce to variation of the second moment. The observed shape of the tail and the orientational dependence of its parameters are explained on the basis of a self-consistent fluctuating-local-field theory. Nonlinear integral equations are derived for the correlation functions, taking into account the changes of the actual number of nearest neighbors caused by the anisotropy of the dipole-dipole interaction and the contribution of lattice sums with loops. The equations are solved numerically. Good agreement is obtained for the computed dropoffs of the free precession, the NMR spectra, and the cross-polarization rates with the experimental results. (C) 1999 American Institute of Physics. [S1063-7761(99)02401-4].
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