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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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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.
Journal cover image

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