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TMF, 2001, Volume 126, Number 2, Pages 325–336 (Mi tmf434)  

This article is cited in 3 scientific papers (total in 3 papers)

A Monte Carlo study of the dependence of the growth parameter for trees on the lattice dimension in the Eden model

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 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 $d\geq3$, the computed values of the growth parameter for trees agree with the values that we derived earlier by the expansion in inverse powers of $2d-1$.

DOI: https://doi.org/10.4213/tmf434

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English version:
Theoretical and Mathematical Physics, 2001, 126:2, 270–279

Bibliographic databases:

Received: 24.06.2000
Revised: 25.10.2000

Citation: V. E. Zobov, M. A. Popov, “A Monte Carlo study of the dependence of the growth parameter for trees on the lattice dimension in the Eden model”, TMF, 126:2 (2001), 325–336; Theoret. and Math. Phys., 126:2 (2001), 270–279

Citation in format AMSBIB
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\by V.~E.~Zobov, M.~A.~Popov
\paper A Monte Carlo study of the dependence of the growth parameter for trees on the lattice dimension in the Eden model
\jour TMF
\yr 2001
\vol 126
\issue 2
\pages 325--336
\mathnet{http://mi.mathnet.ru/tmf434}
\crossref{https://doi.org/10.4213/tmf434}
\transl
\jour Theoret. and Math. Phys.
\yr 2001
\vol 126
\issue 2
\pages 270--279
\crossref{https://doi.org/10.1023/A:1005260114182}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000170245600013}


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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, M. A. Popov, “On the Coordinate of a Singular Point of the Time Correlation Function for a Spin System on a Simple Hypercubic Lattice at High Temperatures”, Theoret. and Math. Phys., 131:3 (2002), 862–872  mathnet  crossref  crossref  zmath  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. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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