Finite-size effects in line-percolating systems

Continuous percolation of finite lines randomly distributed in two dimensions is studied numerically. Two finite-size effects in the distributions of critical percolation densities as a function of the system size are clearly distinguished for the first time in this system. The first one is a roundi...

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Bibliographic Details
Published in:Physics letters. A 1991-05, Vol.155 (2), p.174-180
Main Authors: Vanneste, C, Gilabert, A, Sornette, D
Format: Article
Language:English
Subjects:
Condensed matter: structure, mechanical and thermal properties
Equations of state, phase equilibria, and phase transitions
Exact sciences and technology
General studies of phase transitions
Physics
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Summary:Continuous percolation of finite lines randomly distributed in two dimensions is studied numerically. Two finite-size effects in the distributions of critical percolation densities as a function of the system size are clearly distinguished for the first time in this system. The first one is a rounding of the distribution due to the finite size of the system. The second effect is a shift of the percolation threshold average. The rounding is well described by standard finite-size scaling whereas the shift is not and stems from a perimeter over surface correction. The numerical values of the critical exponents governing the rounding and the probability P ∞ for a line to belong to the percolating cluster are found to be in good agreement with theoretical predictions.
ISSN:0375-9601
1873-2429
DOI:10.1016/0375-9601(91)90588-Y