https://doi.org/10.1007/s100510051153
Precise determination of the conductivity exponent of 3D percolation using exact numerical renormalization
1
Institut Universitaire des Systèmes Thermiques Industriels Enrico Fermi 5, 13453 Marseille Cedex 13,
France
2
Scientific Center for Applied Problems of Electrodynamics, 127412 Moscow, Russia
3
Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003, USA
Received:
27
March
1998
Revised:
5
August
1999
Published online: 15 June 2000
We present detailed description of a computer method for
the calculation of the conductivity
of inhomogeneous systems based on an exact renormalization group
transformation. We study by this method the effective conductivity of the
three-dimensional resistor network at the percolation threshold. For
lattices ranging in size from 43 to 1403 we measure the
dissipation, finding 
, where t is the
conductivity exponent and 
is the correlation length exponent.
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 05.70.-a – Thermodynamics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
