Transfer-matrix approach to three-dimensional bond percolation: An application of Novotny's formalism

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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 languageEnglish
Article number016114
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume73
Issue number1
DOIs
Publication statusPublished - Jan 2006

Fingerprint

Transfer Matrix
formalism
Three-dimensional
Percolation Threshold
Finite-size Scaling
Correlation Length
Criticality
Slice
Critical Exponents
exponents
scaling
Unit
thresholds
Arbitrary
estimates
Estimate
Simulation
simulation

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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