Abstract
A transfer-matrix simulation scheme for the three-dimensional (d=3) bond percolation is presented. Our scheme is based on Novotny's transfer-matrix formalism, which enables us to consider arbitrary (integral) number of sites N constituting a unit of the transfer-matrix slice even for d=3. Such an arbitrariness allows us to perform systematic finite-size-scaling analysis of the criticality at the percolation threshold. Diagonalizing the transfer matrix for N=4,5,...,10, we obtain an estimate for the correlation-length critical exponent ν=0.81(5).
| Original language | English |
|---|---|
| Article number | 016114 |
| Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
| Volume | 73 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2006 |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
Transfer-matrix approach to three-dimensional bond percolation : An application of Novotny's formalism. / Nishiyama, Yoshihiro.
In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 73, No. 1, 016114, 01.2006.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Transfer-matrix approach to three-dimensional bond percolation
T2 - An application of Novotny's formalism
AU - Nishiyama, Yoshihiro
PY - 2006/1
Y1 - 2006/1
N2 - A transfer-matrix simulation scheme for the three-dimensional (d=3) bond percolation is presented. Our scheme is based on Novotny's transfer-matrix formalism, which enables us to consider arbitrary (integral) number of sites N constituting a unit of the transfer-matrix slice even for d=3. Such an arbitrariness allows us to perform systematic finite-size-scaling analysis of the criticality at the percolation threshold. Diagonalizing the transfer matrix for N=4,5,...,10, we obtain an estimate for the correlation-length critical exponent ν=0.81(5).
AB - A transfer-matrix simulation scheme for the three-dimensional (d=3) bond percolation is presented. Our scheme is based on Novotny's transfer-matrix formalism, which enables us to consider arbitrary (integral) number of sites N constituting a unit of the transfer-matrix slice even for d=3. Such an arbitrariness allows us to perform systematic finite-size-scaling analysis of the criticality at the percolation threshold. Diagonalizing the transfer matrix for N=4,5,...,10, we obtain an estimate for the correlation-length critical exponent ν=0.81(5).
UR - http://www.scopus.com/inward/record.url?scp=32844472492&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=32844472492&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.73.016114
DO - 10.1103/PhysRevE.73.016114
M3 - Article
AN - SCOPUS:32844472492
VL - 73
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 1
M1 - 016114
ER -