The coordinate of the singular point of generating functions of clusters in the high-temperature dynamics of spin lattice systems with axially symmetric interaction | Научно-инновационный портал СФУ

The coordinate of the singular point of generating functions of clusters in the high-temperature dynamics of spin lattice systems with axially symmetric interaction

Тип публикации: статья из журнала

Год издания: 2003

Идентификатор DOI: 10.1023/A:1025603416535

Ключевые слова: spin dynamics; singular points; expansion over the reciprocal space dimension

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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Издание

Журнал: THEORETICAL AND MATHEMATICAL PHYSICS

Выпуск журнала: Vol. 136, Is. 3

Номера страниц: 1297-1311

ISSN журнала: 00405779

Место издания: NEW YORK

Издатель: MAIK NAUKA/INTERPERIODICA/SPRINGER

Авторы

  • Zobov V.E. (Kirenskii Institute of Physics,Siberian Branch,RAS)
  • Popov M.A. (Krasnoyarsk State University)

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