Critical behavior of the two-dimensional first passage time
Publication
, Journal Article
Chayes, JT; Chayes, L; Durrett, R
Published in: Journal of Statistical Physics
December 1, 1986
We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probability p and 1-p, respectively. We prove that as the zero-time bonds approach the percolation threshold pc, the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeys ξ(p) ∼|p-pc|-v, then the first passage time constant satisfies μ(p)∼|p-pc|v. At pc, where it has been asserted that the first passage time from 0 to x scales as |x| to a power ψ with 0<ψ<1, we show that the passage times grow like log |x|, i.e., the fluid spreads exponentially rapidly. © 1986 Plenum Publishing Corporation.
Duke Scholars
Published In
Journal of Statistical Physics
DOI
EISSN
1572-9613
ISSN
0022-4715
Publication Date
December 1, 1986
Volume
45
Issue
5-6
Start / End Page
933 / 951
Related Subject Headings
- Fluids & Plasmas
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences
Citation
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ICMJE
MLA
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Chayes, J. T., Chayes, L., & Durrett, R. (1986). Critical behavior of the two-dimensional first passage time. Journal of Statistical Physics, 45(5–6), 933–951. https://doi.org/10.1007/BF01020583
Chayes, J. T., L. Chayes, and R. Durrett. “Critical behavior of the two-dimensional first passage time.” Journal of Statistical Physics 45, no. 5–6 (December 1, 1986): 933–51. https://doi.org/10.1007/BF01020583.
Chayes JT, Chayes L, Durrett R. Critical behavior of the two-dimensional first passage time. Journal of Statistical Physics. 1986 Dec 1;45(5–6):933–51.
Chayes, J. T., et al. “Critical behavior of the two-dimensional first passage time.” Journal of Statistical Physics, vol. 45, no. 5–6, Dec. 1986, pp. 933–51. Scopus, doi:10.1007/BF01020583.
Chayes JT, Chayes L, Durrett R. Critical behavior of the two-dimensional first passage time. Journal of Statistical Physics. 1986 Dec 1;45(5–6):933–951.
Published In
Journal of Statistical Physics
DOI
EISSN
1572-9613
ISSN
0022-4715
Publication Date
December 1, 1986
Volume
45
Issue
5-6
Start / End Page
933 / 951
Related Subject Headings
- Fluids & Plasmas
- 51 Physical sciences
- 49 Mathematical sciences
- 02 Physical Sciences
- 01 Mathematical Sciences