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Zobov, V. E.
Tree growth parameter in the Eden model on face-centered hypercubic lattices / V. E. Zobov, M. A. Popov // Theor. Math. Phys. - 2005. - Vol. 144, Is. 3. - P. 1361-1371, DOI 10.1007/s11232-005-0165-z. - Cited References: 19 . - ISSN 0040-5779

РУБ Physics, Multidisciplinary + Physics, Mathematical
Рубрики:
BRANCHED POLYMERS
   HIGH-TEMPERATURES
   EXPANSION
   CLUSTERS
   SYSTEMS
   TIME
Кл.слова (ненормированные):
Eden model -- number of lattice trees -- Monte Carlo method -- growth parameter -- singular points of generating function -- large-dimension expansion -- face-centered hypercubic lattice -- Eden model -- Face-centered hypercubic lattice -- Growth parameter -- Large-dimension expansion -- Monte Carlo method -- Number of lattice trees -- Singular points of generating function
Аннотация: In the Eden model, we investigate how the tree growth parameter depends on the space dimension d for face-centered hypercubic lattices. We find the first three terms of the 1/d-expansion for this parameter directly from the generating function without calculating the number of trees because the growth parameter is the reciprocal coordinate of the singular point of the tree generating function. The same growth parameter was calculated by computer experiment where the ratios between the numbers of trees without intersections and trees without restrictions in the dimensions 3, 4, 6, 8, and 10 were estimated by the Monte Carlo method on face-centered cubic lattices. The results of the two methods agree well. Comparing with the previously performed computer experiment for simple hypercubic lattices, we observe that the values of the singular exponents for the tree generating functions are close for two different types of lattices.

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Держатели документа:
RAS, Siberian Branch, Kirenskii Inst Phys, Novosibirsk, Russia
Krasnoyarsk State Univ, Krasnoyarsk, Russia
ИФ СО РАН
Kirenskii Institute of Physics, Siberian Branch, RAS, Russian Federation
Krasnoyarsk State University, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Popov, M. A.; Зобов, Владимир Евгеньевич
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Zobov, V. E.
A Monte Carlo study of the dependence of the growth parameter for trees on the lattice dimension in the Eden model / V. E. Zobov, M. A. Popov // Theor. Math. Phys. - 2001. - Vol. 126, Is. 2. - P. 270-279, DOI 10.1023/A:1005260114182. - Cited References: 17 . - ISSN 0040-5779

РУБ Physics, Multidisciplinary + Physics, Mathematical
Рубрики:
DIFFUSION-LIMITED AGGREGATION
   BRANCHED POLYMERS
   HIGH-TEMPERATURES
   EXPANSION
   TIME
Аннотация: We use the Monte Carlo method to compute the number of trees with n edges in the Eden model on d-dimensional simple cubic lattices for d = 2, 3, 4, 6, 8, 10. We compare these numbers with the exact data derived by the enumeration method up to n = 12 on the square lattice and up to n = 10 on the cubic lattice. We find that for d greater than or equal to 3, the computed values of the growth parameter for trees agree with the values that we derived earlier by the expansion in inverse powers of 2d - 1.

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Держатели документа:
RAS, Siberian Branch, Kirenskii Phys Inst, Krasnoyarsk, Russia
Krasnoyarsk State Univ, Krasnoyarsk, Russia
ИФ СО РАН
Kirenskii Physics Institute, Siberian Branch, RAS, Krasnoyarsk, Russian Federation
Krasnoyarsk State University, Krasnoyarsk, Russian Federation

Доп.точки доступа:
Popov, M. A.; Зобов, Владимир Евгеньевич
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Zobov, V. E.
Singular points of time-dependent correlation functions of spin systems on large-dimensional lattices at high temperatures / V. E. Zobov // Theor. Math. Phys. - 2000. - Vol. 123, Is. 1. - P. 511-523, DOI 10.1007/BF02551058. - Cited References: 21 . - ISSN 0040-5779

РУБ Physics, Multidisciplinary + Physics, Mathematical
Рубрики:
BRANCHED POLYMERS
   HEISENBERG MAGNET
   EXPANSION
   MODELS
Аннотация: Time-dependent autocorrelation functions are investigated for the Heisenberg model with spins 1/2 on d-dimensional simple cubic lattices of large dimensions d at infinite temperature. The autocorrelation function on the imaginary time axis is interpreted as the generating function of bond trees constructed with double bonds. These trees provide the leading terms with respect to lid for the time-expansion coefficients of the autocorrelation function. The correction terms from branch intersections to the generating function in the Bethe approximation are derived for these trees. A procedure is suggested for finding the correction to the coordinate of the singular point of the generating function (i.e., to the reciprocal of the branch growth-rate parameter) from the above correction terms without calculating the number of trees. The leading correction terms of order 1/sigma(2) (where sigma = 2d - 1) are found for the coordinates of the singular points of the autocorrelation function in question and for the generating function of the trees constructed with single bonds in the Eden model.

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Держатели документа:
RAS, LV Kirensky Phys Inst, Siberian Div, Krasnoyarsk, Russia
ИФ СО РАН

Доп.точки доступа:
Зобов, Владимир Евгеньевич
}
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