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Application of the lattice Green’s function for calculating the resistance of an infinite network of resistors
Open accessAbstract
The resistance between two arbitrary grid points of several infinite lattice structures of resistors is calculated by using lattice Green’s functions. The resistance for d dimensional hypercubic, rectangular, triangular, and honeycomb lattices of resistors is discussed in detail. Recurrence formulas for the resistance between arbitrary lattice points of the square lattice are given. For large separation between nodes the asymptotic form of the resistance for a square lattice and the finite limiting value of the resistance for a simple cubic lattice are calculated. The relation between the resistance of the lattice and the van Hove singularity of the tight-binding Hamiltonian is given. The Green’s function method used in this paper can be applied in a straightforward manner to other types of lattice structures and can be useful didactically for introducing many concepts used in condensed matter physics.
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Cites
Handbook of Mathematical Functions
McQuarrie, D. A. (1966) · American Journal of Physics · doi:10.1119/1.1972842 · Cited by 40,433
Kirkpatrick, S. (1973) · Reviews of Modern Physics · doi:10.1103/revmodphys.45.574 · Cited by 5,260
Cited by
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Blinder, P., Tsai, P. S., Kaufhold, J. P., Knutsen, P. M., Suhl, H., & Kleinfeld, D. (2013) · Nature Neuroscience · doi:10.1038/nn.3426 · Cited by 573
Theory of resistor networks: the two-point resistance
Wu, F. Y. (2004) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/37/26/004 · Cited by 329
Metadata
- Authors
- Cserti, J.
- Venue
- American Journal of Physics
- Published
- 2000-10-01
- Volume
- 68
- Issue
- 10
- Pages
- 896-906
- ISSN
- 0002-9505 (ISSN-L)
- 1943-2909
- OpenAlex
- W2084236827
- Cited by
- 268
- References
- 2
- FWCI
- 2.51
- Type
- journal article
- Language
- en
- Open access
- green
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