Eden model in many dimensions

Giorgio Parisi; Yi Cheng Zhang

doi:10.1103/PhysRevLett.53.1791

Eden model in many dimensions

Giorgio Parisi^*
, Yi Cheng Zhang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

Abstract

The Eden model in many dimensions is studied by an exact enumeration method. Our result including the first-order 1d correction has the asymptotic behavior Rn22 ln(n) (1+32d), which does not agree with the naive expectation Rn1d [or d (n1d-1)]. This suggests that when n is large, Rn2 might be a singular function of d. We also present a result on the Cayley tree.

Original language	English
Pages (from-to)	1791-1794
Number of pages	4
Journal	Physical Review Letters
Volume	53
Issue number	19
DOIs	https://doi.org/10.1103/PhysRevLett.53.1791
State	Published - 1984
Externally published	Yes

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10.1103/PhysRevLett.53.1791

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title = "Eden model in many dimensions",

abstract = "The Eden model in many dimensions is studied by an exact enumeration method. Our result including the first-order 1d correction has the asymptotic behavior Rn22 ln(n) (1+32d), which does not agree with the naive expectation Rn1d [or d (n1d-1)]. This suggests that when n is large, Rn2 might be a singular function of d. We also present a result on the Cayley tree.",

author = "Giorgio Parisi and Zhang, \{Yi Cheng\}",

year = "1984",

doi = "10.1103/PhysRevLett.53.1791",

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AU - Parisi, Giorgio

AU - Zhang, Yi Cheng

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N2 - The Eden model in many dimensions is studied by an exact enumeration method. Our result including the first-order 1d correction has the asymptotic behavior Rn22 ln(n) (1+32d), which does not agree with the naive expectation Rn1d [or d (n1d-1)]. This suggests that when n is large, Rn2 might be a singular function of d. We also present a result on the Cayley tree.

AB - The Eden model in many dimensions is studied by an exact enumeration method. Our result including the first-order 1d correction has the asymptotic behavior Rn22 ln(n) (1+32d), which does not agree with the naive expectation Rn1d [or d (n1d-1)]. This suggests that when n is large, Rn2 might be a singular function of d. We also present a result on the Cayley tree.

UR - https://www.scopus.com/pages/publications/25144515032

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DO - 10.1103/PhysRevLett.53.1791

M3 - 文章

AN - SCOPUS:25144515032

SN - 0031-9007

VL - 53

SP - 1791

EP - 1794

JO - Physical Review Letters

JF - Physical Review Letters

IS - 19

ER -

Eden model in many dimensions

Abstract

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