Тип публикации: статья из журнала
Год издания: 2005
Идентификатор DOI: 10.1007/s11232-005-0165-z
Ключевые слова: Eden model; number of lattice trees; Monte Carlo method; growth parameter; singular points of generating function; large-dimension expansion; face-centered hypercubic lattice
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 coПоказать полностьюordinate 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.
Журнал: THEORETICAL AND MATHEMATICAL PHYSICS
Выпуск журнала: Vol. 144, Is. 3
Номера страниц: 1361-1371
ISSN журнала: 00405779
Место издания: NEW YORK
Издатель: CONSULTANTS BUREAU/SPRINGER